Differential Equations Answers

4. dy/dx=2y^2+3xy/x^2

y=\frac{c x^{3}}{1-c x^{2}}\]
y=cx31+cx2
y=−cx31−cx2
y=−cx31+cx2

Which of the following satisfied the Laplace's equation in the plane
1. x^2 + y^2
2. x^2 - y^2
3. x + y
4. x - y

(x^2+y^2)dx − 2xydy=0

−x^2−y^2=cx
−x^2+y^2=cx
x^2+y^2=cx
x^2−y^2=cx

Integration factor

1. (x + 2y) dx + x dy = 0
2. ((x^2) + (y^2) + x) dx + y dy = 0
3. (5y - 6x) dx + x dy = 0
4. (3x - (y^2)) dx - 4xy dy = 0

Exact equations
(e^(x^2)y)(1+2(x^2)y)dx + (x^3)(e^(x^2)y)dy = 0

Integrating factor
1. (2xy) dx + (2(x^2) + 3)dy = 0
Having an integration factor is just a function of y.
2. ((x^2) + 3x + 2) dx + ((x^2) + x + 1) dy = 0
Having an integration factor is just a function of (x + y)

2. Solve the initial value problem (1+y^2)dx+(1+x^2)d,y(0)=−1

Tan^−1 x−tan^−1 y=−π/4
Tan^−1 x+tan^−1 y=−π/4
Tan^−1 x+tan^−1 y=−π/4
-Tan^−1 x−tan^−1 y=−π/4

if Uxx + Uyy=0 in x^2 + y^2=1 and U = 3+x+y find U(1/2, 1/2)
A)0
B)2
C)3
D)4

1. Find the solution of y′=2xy^2

y=1/2x(1−y^2)
y=1/2x(1+y^2)
y=1/2(1−y^2)
y=1/2x^2(1−y^2)

Solve the general solution of dy/dx =ex + x + sinx

dy/dx+2y=2x^2+3

yP(x)=x^2−x+2
yP(x)= x^2+x+2
yP(x)=− x^2−x+2
yP(x)=− x^2−x−2