MTH232 TMA SOLUTION 2019_2

Course Code
mth232


Question
Find the general solution of \(y'+2y=x^3 e^{-2x}\)

Answer
\(y=e^{-2x} (x^{4/4}+c)\)



Question
Find the solution of the initial value problem \(dy/dx=12x^3-2 \sin⁡ x\), y(0)=3

Answer
\(y=3x^4+2 \cos⁡ x+1\)



Question
Solve the initial value problem \( (\cos⁡ x \sin⁡ x-xy^2)dx+y(1- x^2 y)dy=0\), y(0)=2

Answer
\(y^2 (1-x^2 )-\cos^2⁡ x=c\)



Question
Which of the following differential equations are seperable (i) \(\frac{dy}{dx}=xy\) (ii) \(\frac{dy}{dx}=x+y\) (iii) \(\frac{dy}{dx}=xy+y\)

Answer
Equations (i) and (iii) only



Question
Obtain the solution of the equation\( xy'=4y\)

Answer
\(y=cx^4\)



Question
Solve the equation dy/dx=sin⁡5x

Answer
y=-1/5 cos⁡5x+c



Question
The solution of the initial value problem dy/dx=-x/y, y(4)=3 is

Answer
\(x^2+y^2=25\)



Question
Find the distance which an object falls under gravity in t seconds if it starts from rest

Answer
\(x=1/2 gt^2\)



Question
Solve \(\frac{ d y}{dx}+\frac{1}{2}y=\frac{3}{2}\)with y(0)=2

Answer
\(y=3-e^\frac{1}{2}x\)



Question
Solve the initial value problem \(\frac{d y}{d x}=2x+3, y(1)=2\)

Answer
\(y=x^{2}+3x-2\)


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