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Find the function satisfying the differential equation

f'(t) - f(t) = 4 t

and the condition f(3)=6. 

f(t)= 

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Find the function satisfying the differential equation

y' - 4 y = 9 e^{7 t}

and y(0) = 1. 

y= 

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Solve the following initial value problem: 

t \frac{dy}{dt} + 5 y = 2 t

with y(1) = 6 . 
y = . 

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Solve the following initial value problem: 

\frac{dy}{dt} + 0.3 ty = 5 t

with y(0) = 3 . 
y =

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Solve the initial value problem 

10 (t + 1) \frac{dy}{dt} - 9 y = 9 t,


for t > -1 with y(0) = 13. 
y =

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Solve the initial value problem

\frac{dx}{dt} + 2 x = \cos(2 t)

with x(0) = -3. 
x(t)= 

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Find the particular solution of the differential equation

\frac{dy}{dx} + y\cos(x) = 8\cos(x)

satisfying the initial condition y(0)=10. 
Answer: y(x)= .

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Solve the initial value problem 

\frac{dy}{dt} - y = 4 \exp(t) + 27 \exp(4 t)

with y(0) = 8. 
y = 

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