{y}{\left({x}^{2}-{1}\right)}{\left.{d}{y}\right.}+{x}{\left({y}^{2}+{1}\right)}{\left.{d}{x}\right.}={0}

Tazmin Horton

Tazmin Horton

Answered question

2021-09-09

y(x21)dy+x(y2+1)dx=0

Answer & Explanation

Ayesha Gomez

Ayesha Gomez

Skilled2021-09-10Added 104 answers

Solve the separable equation x (y(x)2+1)+dy(x)dx(x21)y(x)=0:
Solve for dy(x)dx:
dy(x)dx=x(y(x)2+1)(x21)y(x)
Divide both sides by y(x)2+1y(x):
dy(x)dxy(x)y(x)2+1=xx21
Integrate both sides with respect to x:
dy(x)dxy(x)y(x)2+1dx=xx21dx
Evaluate the integrals:
12log(y(x)2+1)=12log(x21)+c1, where c1 is an arbitrary constant.
Solve for y(x):
y(x)=e2c1x2+1x21ory(x)=e2c1x2+1x21
INTERMEDIATE STEPS:
Solve for y(x):
12log(y(x)2+1)=12log(x21)+c1
Hint: Multiply both sides by a constant to simplify the equation.
Multiply both sides by -2:
log(y(x)2+1)=log(x21)2c1
Hint: Eliminate the logarithm from the left hand side.
Cancel logarithms by taking exp of both sides:
y(x)2+1=e2c1x21
Hint: Isolate terms with y(x) to the left hand side.
Subtract 1 from both sides:
y(x)2=e2c1x211
Hint: Eliminate the exponent on the left hand side.
Take the square root of both sides:

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?