Differential Equations Answers

P2-xp-q=0 solve by charpit method

y'''' + 3y''' + 3y' + y = x*e^(-x) + x*cosx - 7 + x^(2) *e^(-x) *sinx

separate the differential equation into variables

2x²yy^,=1+x²

Reduce the homogeneous equation to the separated one

(x+y)dx+(y-x)dy=0

solve the equation in exact differentials

(y²-1)dx+(2xy+3y)dy=0

Solve the equation in exact differentials:

(y-3x²)dx+(x-4y)dy=0

Solve the equation in exact differentials:

(x²+y)dx+(x-2y)dy=0

Solve the first order linear inhomogeneous differential equation using the Bernoulli method:

y^,+(3y/x)=(1/x³)

Solve the first order linear inhomogeneous differential equation using the constant variation method:

y^,-(2y/x)=-(3/x²)

Verify that the given differential equation is an exact: 

(y²-1)dx+(2xy+3y)dy=0