Differential Equation

For the differential equation $\dfrac{d^{3} y}{d x^{3}}+\cos \left(\dfrac{d^{2} y}{d x^{2}}\right)=0$, which of the following is true ?

The integrating factor of the differential equation $x \dfrac{d y}{d x}+2 y=x^{2} \log x$ is

The degree of the differential equation $\dfrac{d^{2} y}{d x^{2}}+3\left(\dfrac{d y}{d x}\right)^{2}=x^{2} \log \left(\dfrac{d^{2} y}{d x^{2}}\right)$ is

The money invested in a company is compounded continuously. If $R s 400$ invested today becomes ₹800 in 6 years, then at the end of 30 years, it will become (in ₹)

The bacteria increase at the rate proportional to the number of bacteria present. If the original number N doubles in 8 hours, then the number of bacteria in 24 hours will be

An ice ball melts at the rate which is proportional to the amount of ice at that instant. Half of the quantity of ice melts in 15 minutes. $x_{0}$ is the initial quantity of ice. If after 30 minutes the amount of ice left is $\mathrm{kx}_{0}$, then the value of $k$ is

The degree and order of the differential equation ${\left[ 1+{\left( \dfrac{dy}{dx} \right)}^{3} \right]}^{\dfrac{7}{3}}=7\left( \dfrac{d^{2}y}{dx^{2}} \right)$ respectively are

If $\sin x$ is the integrating factor (IF) of the linear differential equation $\dfrac{dy}{dx}+Py=Q$ then $P$ is

Find the degree of the differential equation

If $\dfrac{d y}{d x}=y+5$ and $y(0)=4$ then $y(\log 2)$ is equal to

The differential equation of $3 y=\sqrt[3]{x+c}$ is

The order and degree of the differential equation $3-\left(\dfrac{d^{3} y}{d x^{3}}\right)^{\dfrac{7}{3}}=\left(\dfrac{d y}{d x}\right)^{5}$ are respectively

The rate of disintegration of a radioactive element at any time is proportional to its mass at that time, where $k$ $(k > 0)$ is the constant of proportionality. The time during which an original mass of 1.5 gm will disintegrate to a mass of 0.5 gm is . . .

The order and degree of the differential equation $\sqrt{\dfrac{d y}{d x}}-4 \dfrac{d y}{d x}-7 x=0$ is respectively

The differential equation $x \dfrac{d y}{d x}=2 y$ represents $\_\_\_\_$