Question

(x+e^{y})dy/dx=xe^{-y}-1

Answer #1

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

1.Solve the following initial value problem
a) dy/dx= y2/(x-3), with y(4)=2
b) (sqrt(x)) dy/dx = ey+sqrt(x), with y(0)= 0
2. Find an expression for nth term of the
sequence
a) {-1, 13/24, -20/120, 27/720, ...}
b) {4/10, 12/7, 36/4, 108, ...}

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

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 following ODE's/ IVP's
y'=1/xsin(y)+2sin(2y)
Hint: consider x=x(y) and dx/dy=1/(dx/dy)=1/y'

Homogenous Differential Equations:
dy/dx = y - 4x / x-y
dy/dx = - (4x +3y / 2x+y)

Homogeneous Differential Equations:
dy/dx = xy/x^(2) - y^(2)
dy/dx = x^2 + y^2 / 2xy

Solve the given differential equation
y-x(dy/dx)=3-2x2(dy/dx)

Calculate the iterated integral.
16
1
4
x
y
+
y
x
dy dx
1

Use implicit differentiation to determine dy/dx given the
equation e^x⋅y^3+x^4=sin(y)
dy/dx=

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