Recent questions and answers in Differential Equations

A first-order ordinary differential equation is given as follows:$$\dfrac{d y}{d x}+x^{2} y=0$$Which ONE of the following options CORRECTLY represents the characteristics...

​​​​For the ordinary differential equation $\frac{d^{2} y}{d x^{2}}+4 y=0$, the general solution is$y=c_{1} \cos 2 x+c_{2} \sin 2 x$$y=c_{1} \cosh 2 x+c_{2} \sinh 2 x$$y=...

A tank has inflow, outflow and stirring mechanism. Initially, the tank holds $500 \: L$ of a brine solution of concentration $200 \mathrm{~g} / \mathrm{L}$. At $t=0$, an ...

Consider the equation $\frac{d y}{d x}-x^{2}+e^{x}=0$; with $y=1$ at $x=0$.The value of $y$ at $x=1$ is ________ $\text{(rounded off to 2 decimal places)}$.Take the value...

Which one is the solution $y(x)$ for the following ordinary differential equation and the specified boundary conditions?\[\frac{d^{2} y}{d x^{2}}-3 \frac{d y}{d x}+2 y=2 ...

Given are two ordinary differential equations$\mathrm{P}: \frac{d y}{d x}+x=x \sin y$$\mathrm{Q}: \frac{d y}{d x}+x y=e^{x} y$The correct choice is$\mathrm{P}$ is linear;...

Second order ordinary differential equation $\frac{d^{2} y}{d x^{2}}-\frac{d y}{d x}-2 y=0$ has values $y=2$ and $\frac{d y}{d x}=1$ at $x=0$. The value of y at $x=1$ ...

The ordinary differential equation\[\frac{d y}{d x}=x^{2} y\]has $y$ as the dependent variable and $x$ as the independent variable. Which of the following classification(...

Consider a function $y=f(x)$ which satisfies the following equation:$\frac{d^{2} y}{d x^{2}}-\frac{d y}{d x}=0$ As $x \rightarrow-\infty, y=1$, and at $x=0, y=2$.The valu...

Given, $y=f(x) ; \frac{d^{2} y}{d x^{2}}+4 y=0 ; y(0)=0 ; \frac{d y}{d x}(0)=1$. The problem is a/aninitial value problem having solution $\mathrm{y}=x$boundary value pro...