I need help with problem 4 solving the exact differential equation and finding the integrating factor. C(8)318 3192aySy2xyPROBLEMS (Exact Equations).Find the value of b such that the following equations are exact and then find their1general solution.(a) (xy² + bx²y) + (x + y)x²y' = 0,(b) (ye2y + x) + bxe²yy' = 0.2: Find the general solution to the following differential equations.(a) (e* sin(y) - 2ysin(x)) + (ecos (y) +2cos(x)) y' = 0,(b) (2xy² + 2y) + (2xy + 2x)y' = 0,Y(c) ( + 6x) + (ln(x) — 2)y' = 0,-(d) (xln(y) + xy) + (yln(x) + xy)y' = 0,(e) (2x + 2y) + (2x - 2y)y' = 0.3: Solve the following first order differential equations by first finding the integratingfactor.1(1) (2xy² + y) + (2y³ − x)y' = 0(2) (2x+tan y) + (x-r²tan y)y' = 0(3) x²y³ + x1 + y²)y' = 0(4) (siny - 2e-sinx) + (cosy+2e) y' = 0Cos/x)

The given differential equation is sinyy-2e-x sinx+cosy+2e-xcosxyy'=0. We have to solve the…

Answered: Cos/x (cos y +2e) y = 0 (3) x²y3³+1+…

Math

Advanced Math

Cos/x (cos y +2e) y = 0 (3) x²y3³+1+ y²)y' = 0 (4) (siny - 2e- sinx) + (cos y+2 Y

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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