Differential Equations - Calculus - Mathematics Previous Year Questions

General solution of differential equations

$\frac{d y}{d x}+y=1(y \neq 1)$ is

The integrating factor of the differential equation

$x \cdot \frac{d y}{d x}+2 y=x^2$ is $(x \neq 0)$

The solution of the differential equation $x \frac{d y}{d x}-y=3$ represents a family of

The equation of the curve passing through the point \((1,1)\) such that the slope of the tangent at any point \((x, y)\) is equal to the product of its co-ordinates is

The integrating factor of the differential equation \(\left(2 x+3 y^2\right) d y=y d x(y>0)\) is

The order of the differential equation \(y=C_1 e^{C_2+x}+C_3 e^{C_4+x}\) is

The order of the differential equation obtained by eliminating arbitrary constants in the family of curves \(c_1 y=\left(c_2+c_3\right) e^{x+c_4}\) is

The general solution of the differential equation \(x^2 d y-2 x y d x=x^4 \cos x d x\) is

The curve passing through the point \((1,2)\) given that the slope of the tangent at any point \((x, y)\) is \(\frac{3 x}{y}\) represents

Solution of differential equating \(x d y-y d x=0\) represents

The number of solutions of \(\frac{d y}{d x}=\frac{y+1}{x-1}\), when \(y(\mathrm{l})=2\) is

The solution of the differential equation \(\frac{d y}{d x}=(x+y)^2\) is

If \(\frac{d y}{d x}+\frac{y}{x}=x^2\), then \(2 y(2)-y(1)=\)

The sum of the degree and order of the differential equation \(\left(l+y_1^2\right)^{2 / 3}=y_2\) is

If \(y(x)\) is the solution of differential equation \(x \log x \frac{d y}{d x}+y=2 x \log x, y(e)\) is equal to

The degree of the differential equation \(1+\left(\frac{d y}{d x}\right)^2+\left(\frac{d^2 y}{d x^2}\right)^2=\sqrt[3]{\frac{d^2 y}{d x^2}+1}\) is

If a curve passes through the point \((1,1)\) and at any point \((x, y)\) on the curve, the product of the slope of its tangent and \(x\) coordinate of the point is equal to the \(y\) coordinate of the point, then the curve also passes through the point