12 - Differential Equations Questions Answers

show that the family of the parabolas y^2=2cx+c^2 is self - orthogonal

Asked By: MAGDY MOHMMAD 1 year ago

show that the family of the parabolas y^2=2cx+c^2 is self - orthogonal

Asked By: MAGDY MOHMMAD 1 year ago

What is the solution of Differential Equation y=k(x-k)2?

Asked By: VIJAYENDRA KUMAR 3 year ago
is this question helpfull: 18 5 read solutions ( 3 ) | submit your answer
What is the differential equation of y=ae−x+be−2x+ce−3x
Asked By: MONARK SUTARIYA 4 year ago
x2+2y2=c
Asked By: ALDRIN D SANGMA 4 year ago
Maths >> Calculus >> Differential Equations Engineering Exam
Differential form of ol conics whose axes coincide with the co-ordinate axes??
Asked By: NEHA GUPTA 6 year ago
Answer Strategies and trick by Manish sir (it will help you to solve it by yourself)

let us consider the case of ellipse with x and y axes as their axes

eq. is x2/a2 + y2/b2= 1

on differentiating we get 2x/a2 + 2yy'/b2 = 0                                y'is first differential

so yy'/x = -b2/a2

again differentiate and get answer.

You should remember that you should differentiate as many times as the number of constants.

for ex. in the case of parabola only first diffrentiation is sufficient.

now complete it for all conics

Maths >> Calculus >> Differential Equations Engineering Exam
Form DE of all conics whose axes coincide with d co-ordinate axes??
Asked By: NEHA GUPTA 6 year ago

using the transformation x=r cosθ and y=r sinθ,find the singular solutionof the differential equation x+py=(x-y)(p2+1)½           where p=dy/dx

Asked By: DEBANJAN GHOSHAL 6 year ago
Answer Strategies and trick by Manish sir (it will help you to solve it by yourself)

x=rcosθ and y=rsinθ

so dx=-rsinθdθ  and dy = rcosθdθ

so p = -cotθ

so given eq. will become x-cotθy = (x-y)cosecθ

on putting values of x and y we get

0 = r(cosθ-sinθ)/sinθ

so tanθ = 1  so θ = nπ+π/4

so x = rcos(nπ+π/4) and y = rsin(nπ+π/4)

show that the family of parabolas y2=4a(x+a) is self orthogonal.

Asked By: DEBANJAN GHOSHAL 6 year ago
Answer Strategies and trick by Manish sir (it will help you to solve it by yourself)

y2= 4a(x+a)

so 2yy' = 4a so a = yy'/2

on putting a we get y2= 4yy'/2(x+yy'/2)

so y2 = yy' (2x+yy')  or y = 2xy' + yy'2    (1)

now on putting -1/y' in the place of y'

we get y2 = -y/y'[2x-y/y']

so -yy'2 = 2xy' - y (2)

similarity of (1) and (2) shows that the given curve is self orthogonal

Maths >> Calculus >> Differential Equations Engineering Exam

Solve: dy/dx =[x√(x^2-1) +y]/(√x^2-1)

Asked By: SUBHADEEP BASU 7 year ago