

Solve the following differential equations 2) v' = 2x² + y2 Ans.: y = xv4lnx+C. ху
Solve the following differential equations.
10. Solve the following differential equations. (a) (x2 - y2) 2 = ry (c) y" – y' cot = cot x (d) - 2y = 23
Solve the differential equations ?
Problems: Solve the following differential equations, 1) V1+x?.y?-3xV/y2 -1=0.
4x - y, = 2x + y. Solve the system of differential equations with initial conditions x(0)=1, y(0)=2.
2. Solve the following second order homogeneous differential equations: a) *+x+2x =0 b) Ö-70+5Q =0 c) y"-6y'+9y=0 d) y"+9y=0.
Solve the given system of differential equations by systematic elimination. = 2x – y dv · = x (x(t), y(t))
7. Solve the following differential equations. dy 2 y= 5x, x>0. + a) dx dx 1+2x 4e', t>0 b) t dt
7. Solve the following differential equations. dy 2 y= 5x, x>0. + a) dx dx 1+2x 4e', t>0 b) t dt
solve the following differential equations
(e* + 2y)dx + (2x – sin y)dy = 0 xy' + y = y? (6xy + cos2x)dx +(9x?y? +e")dy = 0 +2ye * )dx = (w*e * -2rcos x) di
Solve the given system of differential equations by systematic elimination. dx dt = 2x − y dy dt = x (x(t), y(t)) =
Problem 5 (40 pts). Given the system of nonlinear differential equations Se=y+ 2(x2 + y2 - 1) y'= -r + y(x² + y2 - 1) (a) Find its critical point(s). (b) Linearize the system about each critical point. (c) Classify each critical point by discussing the zeros of the corresponding characteristic equa- tion. (d) Solve the linearized systems of differential equations about the critical point(s).
1. Solve the following differential equations: a. xy'=y+Vxy x+2y+3 y'= b. 2x – y +5 x+2y+3 y'= x+2y+5 y cos(x+y)+x+y d. sin(x + y) + y cos(x+y)+x+y C. y'=