Differential Equations Maths - Differential Equations

$\frac{d y}{d x}=x^2 y+y$

$\frac{d^4 y}{d x^4}+\sin \left(\frac{d y}{d x}\right)=0$

$\frac{d y}{d x}=3 y+\sqrt[4]{1+5\left(\frac{d y}{d x}\right)^2}$

$\sqrt[3]{1+\left(\frac{d y}{d x}\right)^2}=\frac{d^2 y}{d x^2}$

$\left(\frac{d^3 y}{d x^3}\right)^2=\sqrt[5]{1+\frac{d y}{d x}}$

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

$(y-a)^2=b(x+4)$

$4 \frac{d x}{d y}+8 x=5 e^{-3 y}$

$\frac{d y}{d x}+ y \cot x = x ^2 \cot x +2 x$

the hyperbola whose length of transverse and conjugate axes are half of that of the

given hyperbola $\frac{x^2}{16}-\frac{y^2}{36}=k$.

$\left( x +2 y ^2\right) \frac{d y}{d x}= y$, when $x =2, y =1$

y + 1) = c(1 – x – y – 2xy).

$2 e^{\frac{x}{y}} d x+\left(y-2 x e^{\frac{x}{y}}\right) d y=0$, when $y(0)=1$

$\frac{d y}{d x}-3 y \cot x =\sin 2 x$, when $y \left(\frac{\pi}{2}\right)=2$

$y(1+\log x)=(\log x x) \frac{d y}{d x}$, when $y(e)= e ^2$