Question

solve for y:

1. dy/dx= xe^y separable

2. x(dy/dx)+3y=x^2 when y(5)=0 1st order linear

Answer #1

Solve the 1st order initial value problem:
1+(x/y+cosy)dy/dx=0, y(pi/2)=0

Solve the following:
(3x^2 - y^2)dx + (xy - x^3y^-1)dy = 0

Solve the separable equation 3xy^2 dy/dx = x^2 + 1 given y(0)
=5
I am getting a general solution of cubed root
x2/2+ln|x|+3c1 when I enter the initial
conditions y(0)=5 the equation is undefined. How do deal with this?
What would the final answer be?
Thanks

Solve: 1.dy/dx=(e^(y-x)).secy.(1+x^2),y(0)=0.
2.dy/dx=(1-x-y)/(x+y),y(0)=2 .

Solve the initial value problems.
1) x (dy/dx)+ 2y = −sinx/x , y(π) = 0.
2) 3y”−y=0 , y(0)=0,y’(0)=1.Use the power series method
for this one . And then solve it using the characteristic
method
Note that 3y” refers to it being second order
differential and y’ first

find the solution of the first order differential equation
(e^x+y + ye^y)dx +(xe^y - 1)dy =0 with initial value y(0)= -1

(x+ey)dy/dx=xe-y-1

Use the method for solving homogeneous equations to solve the
following differential equation.
(9x^2-y^2)dx+(xy-x^3y^-1)dy=0
solution is F(x,y)=C, Where C= ?

Solve the equation.
(2x^3+xy)dx+(x^3y^3-x^2)dy=0
give answer in form F(x,y)=c

Solve the following differential equations.
a.) dy/dx+2xy=x, y(0)=2
b.) ?^2(dy/dx)−?y=−y^2

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