Question

solve the following differential equations or initial value problems answers may be left as implicit solutions (or in terms of an integral).

2yy'+1=y^2 + x y(0)=1

Answer #1

solve the following differential equations or initial value
problems answers may be left as implicit solutions (or in terms of
an integral).
yy'+x=(x^2+y^2)^1/2

solve the following differential equations or initial value
problems answers may be left as implicit solutions (or in terms of
an integral).
y'=5y+e^(-2x)y^(-2) y(0)=2

Solve each of the following equations. Implicit answers are
acceptable.
a.) y'-y= cos(x)
with no initial conditions and:
b.) y'= e(x)y-1
with initial conditions y(0)=0

Series Solutions of Ordinary Differential Equations For the
following problems solve the given differential equation by means
of a power series about the given point x0. Find the recurrence
relation; also find the first four terms in each of two linearly
independed sollutions (unless the series terminates sooner). If
possible, find the general term in each solution.
y"+k2x2y=0, x0=0,
k-constant

Solve the following differential equations
1. cos(t)y' - sin(t)y = t^2
2. y' - 2ty = t
Solve the ODE
3. ty' - y = t^3 e^(3t), for t > 0
Compare the number of solutions of the following three initial
value problems for the previous ODE
4. (i) y(1) = 1 (ii) y(0) = 1 (iii) y(0) = 0
Solve the IVP, and find the interval of validity of the
solution
5. y' + (cot x)y = 5e^(cos x),...

Solve the following initial-value differential
equations using Laplace and inverse transformation.
y''' +y' =0, y(0)=1, y'(0)=2, y''(0)=1

Differential Equations: Use the Laplace transform to solve the
given initial value problem:
y′′ −2y′ +2y=cost;
y(0)=1,
y′(0)=0

solve these differential equations and state the equilibrium
solutions if any exist.
y'= x^2 +2x + 1
f'(x)=e^x +1
y'= sinx + x

Solve the following initial-value differential
equations using Laplace and inverse transformation.
y''-y=delta(t-3), y(0)=0,
y'(0)=1

Solve the following differential equations with initial
conditions:
xy'-y=3xy1/2

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