Show that the solution of differential equation :
\(y=\left( { 2x }^{ 2 }-1 \right) +c{ e }^{ { -x }^{ 2 } }\) is \(\frac { dy }{ dx } +2xy-4{ x }^{ 3 }=0\)

2

(a)

From the differential equation of equation y = a cos2x + b sin2x, where a and b are constant.

2

(a)

Find the sum of the order and degree of the following differential equations :
\(\frac { { d }^{ 2 }y }{ dx^{ 2 } } +\sqrt [ 3 ]{ \frac { dy }{ dx } } +\left( 1+x \right) =0\)

2

(a)

Obtain the differential equation of the family of circles passing through the points (a,0) and (- a, 0).

2

(a)

Solve the differential equation \(\frac { dy }{ dx } ={ e }^{ x-y }+x{ e }^{ -y }\).

2

(a)

Solve the differential equation \(\frac { dy }{ dx } =\sqrt { \frac { 1-\cos { x } }{ 1+\cos { x } } } \)

2

(a)

Solve the differential equation \(\frac { dy }{ dx } =xy+2y\)

2

(a)

Solve the differential \(xdy=\left( \frac { y+1 }{ y } \right) dx\)

2

(a)

Solve the differential equation \(\frac { dy }{ dx } =xy+x+y+1\)

2

(a)

Solve the differential equations
\(\frac { dy }{ dx } =\frac { 1+\cos { 2y } }{ 1+\cos { 2x } } \)

2

(a)

Find the general solution of differential equation \(\frac { dy }{ dx } ={ e }^{ 3x-4y }\)

2

(a)

Find the general solution of differential equation \(\log { \left( \frac { dy }{ dx } \right) } =x+1\)

2

(a)

Find the general solution of differential equation
\(\frac { dy }{ dx } +y={ e }^{ -x }\)

2

(a)

Find the general solution of differential equation
\(x\frac { dy }{ dx } +y={ x }^{ 2 }\).

2

(a)

Find the general solution of the differential equation: \((x-y){dy\over dx}={x+2y}\)

2

(a)