Class 12

Math

Calculus

Differential Equations

The solution of the differential equation ${1+x(x_{2}+y_{2}) }dx+{(x_{2}+y_{2}) −1}ydy=0$ is equal to

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Solve $(x−1)dy+ydx=x(x−1)y_{31}dx˙$

Let $f$ be a real-valued differentiable function on $R$ (the set of all real numbers) such that $f(1)=1.$ If the $y−∈tercept$ of the tangent at any point $P(x,y)$ on the curve $y=f(x)$ is equal to the cube of the abscissa of $P,$ then the value of $f(−3)$ is equal to________

Solution of differential equation x2=1+(xy)−1dydx+(xy)−2(dydx)22!+(xy)−3(dydx)33!+......... is

Find the real value of $m$ for which the substitution $y=u_{m}$ will transform the differential equation $2x_{4}ydxdy +y_{4}=4x_{6}$ in to a homogeneous equation.

What is the solution of the equationln(dydx)+x=0?

The solution of dydx=ex(sin2x+sin2x)y(2logy+1) is

The function $y=f(x)$ is the solution of the differential equation $dxdy +x_{2}−1xy =1−x_{2} x_{4}+2x $ in $(−1,1)$ satisfying $f(0)=0.$ Then $∫_{23}f(x)dx$ is

A normal at $P(x,y)$ on a curve meets the x-axis at $Q$ and $N$ is the foot of the ordinate at $P˙$ If $NQ=1+x_{2}x(1+y_{2}) $ , then the equation of curve given that it passes through the point $(3,1)$ is