7.Obtain the particular solution of (1 – xy)-2dx + [y? + x²(1 – xy)-²]dy = 0 when x = 2, y = 1

Q: 1. Determine the general solution of the following nonhomogeneous linear equations. dy 1. dx ex 2+ y…

A: Second order linear non−homogeneous differential equation with constant coefficients A second order…

Q: 10.Obtain the general solution of y(8x – 9y)dx + 2x(x – 3y)dy = 0

A: First we find tha integrating factor of given differential eq then we get exact differential eq.So,…

Q: Find an explicit solution of the given initial-value problem. √₁-y² dx - √√₁-x² dy = 0, y(0) = 1/2…

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Q: 6. Find a particular solution to the inhomogeneous equation y" – 9y' + 8y = e2* |D in the form y(x)…

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Q: 1. Show that y(x) = c; sin 2x + c₂ cos 2x is a solution to y + 4y = 0.

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Q: 2. Obtain the particular solution when x = 0 and y = 1 (2 xy + x + x*) dc + x²) dy = 0 - (1 + 4 |

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Q: Solve the IVP u® +u"=e*-2tx with y(0)=1, y'(0)=0, y"(0)=1 (where t is a real constant)

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Q: Find a particular solution to y" + 5y' + 6y = lte".

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Q: I. Find the general solution of the following: 1. dx dy -2x + 3x² dy 2. dx = 3e-2x 3. (x² + 5)dx –…

A: Differential equation problem....

Q: Find the general solution of (xy + 4x)y = 5y² + 4xy². a) Oy + 12y- = -5 In |x| – 16x + C b) Oy - 4y-…

A: First order non linear ordinary differential equation.

Q: 2. Obtain the general solution of x³y" + 3x2y' + x (+x) y = 0. Hint: The differential equation is…

A: Given: x3y''+3x2y'+x14+xy=0 To find: Bessel function.

Q: 1. Find the general solution of dy dx + y = x

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Q: Solve the fallowing Cauchy problem U4- Au + cu=0 in R" x(0, 0) On IR"x{t=0}. U = where c is a…

A: Given the Cauchy problem as ut-∆u+cu=0,             in ℝn×0,∞                (1) re-write the…

Q: 1. Consider the DE dy dz dy -5- + 4y = 8x + 2, y(0) = 1 dr Verify that y = Ae + 2x + 3 is a solution…

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Q: Find general solution of (4x + 6y)dx + (8x + 12y − 6)dy = 0 (DE WITH COEFFICIENTS LINEAR IN 2…

A: We have to solve given problem:

Q: Find the general solution of the nonhomogeneous equation y4) + 2 y "+y=cos( 3 x) + 2 1 a) y =C,…

A: We will find out the required solution.

Q: 2. Find the general solution of d²y dy +5- dr.² dx 6y=0

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Q: 1. Show that y = ze* + e-2* is a solution of y' + 2y = 2e*. 3

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Q: 1. Find the general solution of dy dx +y=x

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Q: 3. Find for the simplified general solution of (1 + x³)dy – x²ydx = 0 a. Iny =In(1 + x³) + C b. Iny…

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Q: 2.8 Find the particular solutions of a) y - x- = 1 + x² dy 2 dy = dx b) (1 + x²)2 dy dx dy dx dy c)…

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Q: 1. (a) Show that (x) x² is an explicit solution to dy X- = 2y dx on the interval (-∞, ∞). (b) Show…

A: An explicit solution is any solution that is given in the form y=y(x)

Q: 1 Find the complete solution of y" - 2y' + 2y =x + e* cos x.

A:

Q: Find an explicit solution of the given initial-value problem. √₁-y² dx - √1-x² dy = 0, y(0) = -1/ 1-…

A: The given differential equation,1-y2dx-1-x2dy=0, y0=12

Q: the solution to the IVP(x2+y2)dy/dx+xy=0 with y(0)=2 is

A: Given DE is x2+y2dydx+xy=0  and y(0)=2 find the solution of the DE

Q: +2. =0 by Find the solution of the PDE dx? dy² variable separable method

A: Given problem is :

Q: Find an explicit solution of the given initial-value problem. x2 dy = y - %3D у — ху, у(-1) %3D -1…

A: Firstly we will solve the given differential equation by using variable separable form then…

Q: 2 (a) Find the particular solution of the following equation satisfying the given initial…

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Q: Find an explicit solution of the given initial-value problem. +²dy x=y=xy, y(-1) = -4 dx y =

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Q: 2. Find the particular solution of (xy + x)dx = (x?y² + x² + y² + 1)dy satisfying the initial…

A: Using Variable Separable Method

Q: 8. Find the particular solution that satisfies the initial condition. y'+y = 6e*, Initial Condition:…

A: Find the particular solution

Q: Find an explicit solution of the given initial-value problem. √2 √₁-y² dx - 1- √1-x² dy = 0, y(0) =…

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Q: 4. Find the solution of the following set of simultaneous equations by LT with initial conditions…

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Q: 2. Find the particular solution of Vx2 + y2 )dx – x dy = 0 ; y = 1 when x V3. -

A: Given differential equations homogeneous differential equation of first order we will do the…

Q: 4. Find the general solution of this DE using INSPECTION. dadx + aydy +(X² + y?)dx = 0

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Q: 6. Find the general solution of 2x(3x + y – ye-**)dx + (x² + 3y2 + e-**)dy = 0

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Q: (2xy +y) dx + (x²- x ) dy = 0

A: Given: (2xy+y)dx+(x2-x)dy=0, y(0)=e

Q: 4. Find the general solution of y"- 4y – 12y = 5le sin(3r).

A: To find - Find the general solution of y'' - 4y' - 12y = 51exsin3x

Q: 6. Find the particular solution of 2xydx + (y² – x²)dy = 0 ;where y = 2 and x =

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Q: In this problem, y = 1/(1 + c,e) is a one-parameter family of solutions of the first-ord initial…

A: Given: y=11+c1e-x, y0=-17 For finding expression of y, first we find value of c1 Now, for finding…

Q: Find the general solution of the nonhomogeneous equation y " - 3 y "+4 y ' – 12y =e + 2 1 3* + C,…

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Q: (1 – xy)-2 dx + [y² + x²(1 – xy)¯2] dy = 0; when x = 4, y = 1.

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Q: = 4 is 3. The nontrivial analytical solution of +x=with x(0) = (a)3-e (b) 3+e (c) 3+es (d)-3+e…

A: NOTE: Refresh your page if you can't see any equations. . compare this DE with   so here we have

Q: 3. Find the solution of the initial-value problem d'y_3dy +2y=e* dx y(0)=1, y'(0) = 0 dx Using…

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Q: (3) 1. Solve the IVP u +u"=e*-7 tx with y(0)=1, y'(0)=0, y"(0)=1 (where t is a real constant)

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Q: 8. Find the solution y(t) of th d³y dy - 2y% = dt dt3

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Q: Find an explicit solution of the given initial-value problem. dy y (2) = 2 %3D dx x2-1

A: An equation which involves the derivative or differential coefficient is called differential…

Q: 2. Obtain the general solution of: xy dx – (x² + 3y²) dy = 0

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