Differential Equation

Study Material (PDF)
Self Assesment
Study Material (PDF)
Self Assesment

Click on each question to see answer & solution.

Question No: #21

Find the differential equation of all curves satisfying equation `k(y+k)^2=x^3`, where `k` is a parameter.
Ans: `144xy^2(\frac{dy}{dx})^10+648x^2y(\frac{dy}{dx})^8+729x^3(\frac{dy}{dx})^6=64x^3(\frac{dy}{dx})^12`
SEE SOLUTION

Question No: #22

Find the differential equation of `ax+by+c=0` by removing three arbitrary constants `a, b, c`.
Ans: `\frac{d^2y}{dx^2}=0`
SEE SOLUTION

Question No: #23

Find the differential equation of `x^2+y^2=2ax` where `a` is a parameter.

Question No: #24

Show that the differential equation of `\frac{x^2}{a^2+\lambda}+\frac{y^2}{b^2+\lambda}=1` (`a, b` fixed constants & `\lambda` arbitrary constant) is `(x+y\frac{dy}{dx})(x\frac{dy}{dx}-y)=(a^2-b^2)\frac{dy}{dx}`

Question No: #25

Find general solution of `\frac{dy}{dx}+y\ g'(x)=g(x)\cdotg'(x)`

Question No: #26

If `\frac{dy}{dx}+2x=e^{3x}` then find `y`

Question No: #27

Find the values of `k` for which `y=k\sinx` satisfies the differential equation `\frac{d^2y}{dx^2}+2y=2`
Ans: `\frac{2}{sinx}`
SEE SOLUTION

Question No: #28

Solve: `(1+\cosx)dy=(1-\cosx)dx`
Ans: `y=2\tan\frac{x}{2}-x+c`
SEE SOLUTION

Question No: #29

Solve: `\frac{dy}{dx}=e^{x+y}+x^2e^y` (alt: `\frac{dy}{dx}=e^{x-y}+x^2e^{-y}`)

Question No: #30

Solve: `\frac{dy}{dx}=e^{4x-3y}`; given `y(0)=0`