Differential Eq...

Find the value of \(y(\frac{1}{2})\) for the differential equation \(d y=x \sec \frac{y}{x} d x+\frac{y}{x} d x\)with initial condition \(y(1)=\) \(\frac{\pi}{2 }?\)

Find the general solution of given differential equation \(\frac{x d y}{d x}+3 y=4 x^{3}\) ?

Integrating factor of \(\left(1-x^{2}\right) \frac{d y}{d x}-x y=1\) is:

Find the degree and order of given equation:

\(\frac{d^{3} y}{d x^{3}}=\frac{d^{2} y}{d x^{2}}+\sin 60^{\circ} \)

General solution of \(\left(x^{2}+y^{2}\right) d x-2 x y d y=0\) is:

Find general solution of \(\frac{\mathrm{dx}}{\mathrm{dy}}=\left(1+\mathrm{x}^{2}\right)\left(1+\mathrm{y}^{2}\right)\)

Form the differential equation of \(y=a e^{3 x} \cos (x+b)\) Where \(y^{\prime}=\frac{d y}{d x}\) and \(y^{n}=\frac{d^{2} y}{d x^{2}}\)

The solution of the differential equation \(\frac{\mathrm{dy}}{\mathrm{dx}}=\sec \left(\frac{\mathrm{y}}{\mathrm{x}}\right)+\frac{\mathrm{y}}{\mathrm{x}}\) is:

The degree of the differential equation

\(\frac{d^{2} y}{d x^{2}}+3\left(\frac{d y}{d x}\right)^{2}=x^{2} \log \left(\frac{d^{2} y}{d x^{2}}\right)\)

The differential equation representing the family of curves \(y=a \sin (\lambda x+a)\) is:

The differential equation of all parabolas whose axis is \(y\)-axis is:

The differential form of the equation \(\mathrm{y}^{2}+(\mathrm{x}-\mathrm{b})^{2}=\mathrm{c}\):

General solution of differential equation \(\frac{ dy }{ d x}+ y =1,( y \neq 1)\), is:

Find general solution of \(\left(\mathrm{y} \frac{\mathrm{d} y}{\mathrm{dx}}-\frac{1}{\mathrm{x}}\right)=0\):

Find the degree and order of differential equation:

\(y ^{\prime \prime \prime}-\sin \left(y^{\prime}\right)+y=0\)

The differential equation of the family of curves \(y=c_{1} e^{x}+c_{2} e^{-x}\) is:

The solution of the differential equation \(\frac{\mathrm{d} y}{\mathrm{dx}}=2^{x-1}\) is:

The differential equation representing the family of curves \(y=a \sin (\lambda x+a)\) is:

The differential form of the equation \((y-b)=a \sin x\):

The solution of \(x^{2} \frac{d y}{d x}=x^{2}+x y+y^{2}\) will be:

Solve the differential equation:

\(x d y-2 y d x=0\)

Solve \(x \frac{d y}{d x}-y=x^{2}\) for \(y(2)\), given \(y(1)=1\):

If \(x d y=y d x+y^{2} d y, y>0\) and \(y(1)=1\), then what is \(y(-3)\) equal to?

The general solution of \(\frac{d y}{d x}+y \tan x=2 \sin x\) is:

If \(\frac{d y}{d x}=e^{-3 y}, y=0\) when \(x=5\), value of \(x\) for \(y=5\) is:

Form the differential equation for the family of circle with center \((0,0)\) and radius \(r\), where \(r\) is any constant:

The integrating factor of the differential equation \(2 \mathrm{y} \frac{\mathrm{d} \mathrm{x}}{\mathrm{dy}}+\mathrm{x}=5 \mathrm{y}^{2}\) is, \((\mathrm{y} \neq 0)\):

Find the general solution of the differential equation:

\(\frac{y^{2}}{x^{2}}=\frac{d y}{d x}\)

Form the differential equation of the following \(y^{2}=a\left(b^{2}-x^{2}\right)\):

Solve the differential equation \(\sin x \frac{d y}{d x}+\frac{y}{\sin x}=x \sin x e^{\cot x}\):