Differential Equations · Mathematics · KCET
MCQ (Single Correct Answer)
The solution of $e^{d y / d x}=x+1, y(0)=3$ is
The family of curves whose $x$ and $y$ intercepts of a tangent at any point are respectively double the $x$ and $y$ coordinates of that point 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
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 $$\frac{d y}{d x}+\frac{y}{x}=x^2$$, then $$2 y(2)-y(1)=$$
The solution of the differential equation $$\frac{d y}{d x}=(x+y)^2$$ 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 sum of the degree and order of the differential equation $$\left(l+y_1^2\right)^{2 / 3}=y_2$$ is
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 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
The integrating factor of the differential equation $$\left(2 x+3 y^2\right) d y=y d x(y>0)$$ is
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 order of the differential equation $$y=C_1 e^{C_2+x}+C_3 e^{C_4+x}$$ is
The solution of the differential equation $x \frac{d y}{d x}-y=3$ represents a family of
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 $(x \neq 0)$