Q2/ solve the following equations. (x² + y²)dx + xydy = 0

Q: Use the graphical method to solve the equation.

A: Given, 2x+1+1=x

Q: 1. (2+ y'y' dy 2. [(1+x)? Vxdx

A:

Q: Q4/ solve the following equations. d²y dy + 81 = 0 dx2 dx

A:

Q: (x+xy²)dxte*, ydy=D0

A: Given: x+xy2dx+ex2ydy=0 ⇒x1+y2dx+ex2ydy=0 ⇒ex2ydy=-x1+y2dx ⇒y1+y2dy=-xex2dx

Q: Solve the following D-E 3) + y = y³ dx

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Q: Solve: (4x3y−18x2−y)dx + (x4+3y2−x)dy = 0 a) Check for exactness b) If the equation is exact,…

A: Exact differential equation

Q: Solve for the family of solutions of the following equations. 1. xydx + (x2 + y2)dy = 0 2.…

A: SOLUTION-

Q: Solve the equations by the method of undeterminedcoefficients

A: First, consider the homogeneous case d2ydx2+7dydx=0. We solve the auxiliary equation as…

Q: Solve the following by Substitution Method. (Complete solution) b. dy/dx = (-5x + y)^2 - 4

A: From the given differential equation: dydx=-5x+y2-4...1 Use the substitution method to calculate…

Q: Q3- Solve nonexact D. E x dx+(3y4+y+3x2y2) dy 0.

A:

Q: 1. Solve the following equations: c) (x² - 4xy – 2y²) dx + (y² + 4xy – 2x²) dy = 0 -

A: Given :x2-4xy-2y2dx+y2-4xy-2x2dy=0

Q: Q2: solve the equation dx 2x dy y y 3.

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Q: Solve the following equations: dy dy 12 dr2 9. +4y 0; y(a) -0. y(x)-2 210 da

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Q: W3 y = dy solve for a-w' dw HIN

A: To find: Solve using chain rule for dy/dw

Q: (c) Solve the following IVP by separating variable. 2(y - a)da + (3a + 4r + b)dy = 0 Using initial…

A:

Q: Solve the following d'y 8- + 16y = 9e2 dx? d'y dx4 using the method of undetermined coefficients.

A: The solution is given as

Q: Solve the equation: 8d3y/dx3 -5dy/dx+3y x3, for x, with initial values of (d3y/dx3 (0) = 4) and y…

A:

Q: solve the D. y +8y" +16Y

A: We have to solve the differential equation.                                  y''''+8y''+16y=0 can…

Q: Find the values of "r" for which y(x) = e* solves the equation y" +3y'-4y= 0

A: We have to find the value of r .

Q: Q: Solve : -4t y +2y Jydt = e s(t -3) yco) = 0 , y'co)= 0 %3D

A: Step:-1 Note:- In given problem, the integral you mention has limit "t" and integral is also in the…

Q: Solve: x dy -(3x+5y) + 15y = 0 and write your solution set as a single equation

A: Remember:1.if ax2+bx+c=0Then, x=-b±b2-4ac2a2. If y1 and y2 are general solutions of a differential…

Q: Solve the equation xydx - (x + 2)dy = 0

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Q: Solve the equation by using the method of variation of parameters dy 2dy 22 + 2y = e“ csc x. dx dx2

A: Let us consider the second order differential equation y''+py'+qy=g(t) Determine the complementary…

Q: Solve the equation: ydx + 3x – xy + 2)dy = 0

A: Given: ydx+3x-xy+2dy=0

Q: Q1:- Solve the following DEs:- dy + 2x³y = y³x³ ,33 dx

A:

Q: Solve the following equation for c: 1 2-c-z 2-²-y 1 dz dy da 10

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Q: solve using the appropriate method. y + 3y − 1/ t = t + 2

A: y+3y-1t=t+2y+3y-1t-y+3y=t+2-y+3ySimplify: -1t=t+2-4yMultiply t: -1tt=tt+2t-4ytSimplify: -1=t2+2t-4yt

Q: Find the solution to the Bernoulli Equation. 2x³y = y(y? +3x?)

A: The solution is given as

Q: Q4/ solve the following equations. d²y dy + 81- = 0 dx² dx

A:

Q: a) Find the general solution of the equation d'y dy dr? + 3e* dr by using the method of undetermined…

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Q: Solve for the general solution of the following equations: y(4x + y)dx – 2(x² – y)dy =( а.

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Q: Solve the following DE: 1. (D² – 3D + 2 ) y = 4x?

A: Since you have posted multiple questions, we will solve the first question for you. If you want any…

Q: Solve the initial value problem. d?y = 12 - 24x, y'(0) = 7, and y(0) = dx2 %3D y(x) =O

A: We have to find y

Q: Solve the he (D’+ 4D+4)y(x) = 5e equation y,)-(2x+1)e - y,) (2x+1)e y,(x) (2x-1)e 32

A:

Q: Q1. Find a general solution of the following equation: 2x(dx + dy) + y(dy – 5dx) = 0

A: Here we have,  2x(dx+dy)+y(dy-5dx)=0

Q: 3) Solve the following IVP (y+ Vx2 + yz ) dx – xdy = 0, y(1) = 0

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Q: nd Solve:- Qz: Chassify - 3x dy +(3X+リ』= e

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Q: Q1:- Solve the following DEs:- dy + 2x³y = y³x3 dx

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Q: B- Solve the D.E.: y--e* = 0, y(1)=1 .

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Q: Solve using the method of variation of parameters y" + 3y' + 2y =: 1+ e*

A: Given that: y''+3y'+2y=11+ex

Q: Find the solution using variation of parameters to the diffrential equation (D3 + D)y = sec2x

A: Find the solution using variation of parameters to the diffrential equation (D3 + D)y = sec2x

Q: Solve the equation xd2y/dx2-dy/dx+4x^3y=x^5

A: Consider the provided D.E,

Q: E. Solve the equation x’ydx+(y-x')dy =0.

A: Comparing with the differential equation Mdx+Ndy=0 we have, M=x2y and N=y-x3. So the partial…

Q: y= 2x³-27 3x4 - 2x Find dy da

A: Given: y=2x5-x33x4-2xTo Find: To find dydx.

Q: Q/ Solve the DEs: 1-a+yxdx+(1+x)dy = 0

A: 1-(1+y2)dx+(1+x2)dy=0

Q: Q3) Solve the following equation with Bernoulli equation Method, where dm 4 m³y? dy m

A:

Q: Q#d4 Solve the D.E. y"+ 25y= lo(cosst-asinst)

A: Given: y''+25y=10cos5t-2sin5t, y(0)=1, y'(0)=2