Question

1.Solve the following initial value problem

a) dy/dx= y^{2}/(x-3), with y(4)=2

b) (sqrt(x)) dy/dx = e^{y+sqrt(x)}, with y(0)= 0

2. Find an expression for *n ^{th}* term of the
sequence

a) {-1, 13/24, -20/120, 27/720, ...}

b) {4/10, 12/7, 36/4, 108, ...}

Answer #1

Solve the following initial value problem,
dy/dx = 8cos(x) / (y2 + 4y + 4)
y(π/4) = 4

1)Consider the following initial-value problem.
(x + y)2 dx + (2xy + x2 − 2) dy =
0, y(1) = 1. Let af/ax = (x + y)2 =
x2 + 2xy + y2. Integrate each term of this
partial derivative with respect to x, letting
h(y) be an unknown function in y.
f(x, y) = + h(y)
Solve the given initial-value problem.
2) Solve the given initial-value problem.
(6y + 2t − 3)
dt + (8y + 6t
− 1) dy...

1) Consider the following initial-value problem.
(x + y)2 dx + (2xy + x2 − 2) dy =
0, y(1) = 1
Let af/ax = (x + y)2 = x2 + 2xy +
y2.
Integrate each term of this partial derivative with respect to
x, letting h(y)
be an unknown function in y.
f(x, y) = + h(y)
Find the derivative of h(y).
h′(y) =
Solve the given initial-value problem.
2) Solve the given initial-value problem.
(6y + 2t − 3)
dt...

Solve the Initial Value Problem
(y2 cos(x) − 3x2y − 2x) dx + (2y sin(x) −
x3 + ln(y)) dy = 0, y(0) = e

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

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

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

Solve the given initial-value problem. (x + 2) dy dx + y =
ln(x), y(1) = 10 y(x) =
Give the largest interval I over which the solution is defined.
(Enter your answer using interval notation.)
I =

Solve the initial-value problem.
(x2 + 1)
dy
dx
+ 3x(y − 1) = 0,
y(0) = 4

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 .

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