Does the differential equation $y^{3} d y + (x + y^{2}) d x = 0$ becomes homogeneous if we put $y^{2} = t$ ?

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Solution

Given $y^{3} d y + (x + y^{2}) d x = 0$
If we put $y^{2} = t$
$\Rightarrow 2 y d y = d t$
Consider $y^{3} d y + (x + y^{2}) d x = 0 \Rightarrow \frac{t}{2} d t + (x + t) d x = 0$
An homogenous equation

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Similar questions

Q. Statement 1: The differential equation

y^{3} d y + (x + y^{2}) d x = 0

becomes homogeneous if we put

y^{2} = t

Statement 2: All differential equation of first order and first degree of curves

f (x, y) = 0

becomes homogeneous if we put

y = t x

Q. The solution of the differential equation

y^{3} d y + (x + y^{2}) d x = 0

is:

Q. Solve the homogeneous differential equation:

(x^{2} + y^{2}) d x + 2 x y d y = 0

Q. Check whether the differential equation

(x y) d x - (x^{3} + y^{3}) d y = 0

is homogenous or not ?

Which of the following is a homogeneous differential equation?
(a) (4x +6y+5)dy-(3y+2x+4)dx=0
(b) $x y d x - (x^{3} + y^{3}) d y = 0$
(c) $(x^{3} + 2 y^{2}) d x + 2 x y d y = 0$
(d) $y^{2} d x + (x^{2} - x y - y^{2}) d y = 0$

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Does the differential equation y3dy+(x+y2)dx=0 becomes homogeneous if we put y2=t ?

Given y3dy+(x+y2)dx=0If we put y2=t ⇒2ydy=dtConsider y3dy+(x+y2)dx=0⇒t2dt+(x+t)dx=0An homogenous equation

Does the differential equation $y^{3} d y + (x + y^{2}) d x = 0$ becomes homogeneous if we put $y^{2} = t$ ?

Given $y^{3} d y + (x + y^{2}) d x = 0$
If we put $y^{2} = t$
$\Rightarrow 2 y d y = d t$
Consider $y^{3} d y + (x + y^{2}) d x = 0 \Rightarrow \frac{t}{2} d t + (x + t) d x = 0$
An homogenous equation