Differential Equation

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

Click on each question to see answer & solution.

Question No: #11

Find order & degree of differential equation of `\sqrt{\sinx}(dx+dy)=\sqrt{\cosx}(dx-dy)`.
Ans: Order = 1, degree = 1
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Question No: #12

The differential equation of the family of lines passing through the origin is -- (i) `x\frac{dy}{dx}=y`, (ii) `x+\frac{dy}{dx}=0`, (iii) `\frac{dy}{dx}=x`, (iv) `x\frac{dy}{dx}+y=0`

Question No: #13

Show that `v=A/r+B` satisfies the differential equation `\frac{d^2v}{dr^2}+2/r\cdot\frac{dv}{dr}=0`

Question No: #14

Prove that `x=A\cos\sqrt{\mu}t` is a solution of the differential equation `\frac{d^2x}{dt^2}+\mu\x=0`

Question No: #15

Examine that `y=cx+2c^2` is a general solution of the differential equation `2(\frac{dy}{dx})^2+x\frac{dy}{dx}-y=0`.

Question No: #16

The differential equation representing the family of curves `y^2=2c(x+\sqrt{c})` where `c\gt0` is a parameter. Find the order and degree of this differential equation.
Ans: Order = 1, degree = 3
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Question No: #17

Find the differential equation of all curves given by `y=Ae^{2x}+Be^{-x/2}` where `A` & `B` are non-zero parameters.
Ans: `2\frac{d^2y}{dx^2}-3\frac{dy}{dx}=2y`
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Question No: #18

Find the differential equation of `y=Ax+B/x` by eliminating two arbitrary constants `A` & `B`.
Ans: `x^2\frac{d^2y}{dx^2}+x\frac{dy}{dx}-y=0`
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Question No: #19

Form the differential equation representing family of curves `y=A\cos(x+B)` where `A` and `B` are parameters.
Ans: `\frac{d^2y}{dx^2}+y=0`
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Question No: #20

Form the differential equation from `y=a\secx+b\tanx` where `a` & `b` are arbitrary constants.
Ans: `\frac{d^2y}{dx^2}=y\sec^2x+\tanx\frac{dy}{dx}`
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