Differential Equations Answers

<e> Solve the first order linear inhomogeneous differential equation using the bernoulli method

(2x+1)y^,=4x+2y

<e> Solve using the method of separation of variables the pde partial du/dt+du/dx+2e^tu=0

<e> Solve the first order linear inhomogeneous differential equation using the constant variation method

y^,- (3y/x)=x

(a) The differential equation (2𝑥 2 + 𝑏𝑦 2 )𝑑𝑥 + 𝑐𝑥𝑦 𝑑𝑦 = 0 can made exact by multiplying with integrating factor 1 𝑥 ⁄ 2.

Then find the relation between 𝑏 and 𝑐. (b) Find one fourth roots of unity

verify that -2x^2y+y^2=1 is the implicit solution of the of the differential equation (x^2-y)dy/dx + 2xy=0

determine the general/particular solution for each equation using the applicable solution to equations of order one (separable, homogenous,linear,exact)

3x(xy-2)dx + (x^3=2y)dy = 0

determine the general/particular solution for each equation using the applicable solution to equations of order one (separable, homogenous,linear,exact)

1. (1+y^2)dx + (1=x^2)dy = 0 ; when x = 0, y = 1

Solve:

(𝑥 − 2𝑠𝑖𝑛𝑦 + 3)𝑑𝑥 + (2𝑥 − 4𝑠𝑖𝑛𝑦 − 3)𝑐𝑜𝑠𝑦𝑑𝑦 = 0

(1 + 𝑥^2) (xdy+ydx) =-2yx^2

𝑦′ − 𝑦 = 𝑒2𝑥𝑦3