Solve the following initial value problem for the function y(x). y'=2xy^2;\

Jean Blumer 2021-12-23 Answered
Solve the following initial value problem for the function y(x).
y=2xy2; y(1)=12
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Expert Answer

Bertha Jordan
Answered 2021-12-24 Author has 37 answers
y=2xy2
dydx=2xy2
dyy2=2xdx
=y1=x2+c
1y=x2+c
given y(1)=12
2=1+c
c=3
1y=x23
y=13x2 - is the solution
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GaceCoect5v
Answered 2021-12-25 Author has 26 answers

Solve the separable equation dy(x)dx=2xy(x)2, such that y(1) = 1/2:
Divide both sides by y(x)2:
dy(x)dxy(x)2=2x
Integrate both sides with respect to x:
dy(x)dxy(x)2dx=2xdx
Evaluate the integrals:
1y(x)=x2+c1, where c1 is an arbitrary constant.
Solve for y(x):
y(x)=1x2+c1
Solve for c1 using the initial conditions:
Substitute y(1)=12y(x)=1x2+c1:
1c1+1=12
Solve the equation:
c1=3
Substitute c1=3y(x)=1x2+c1:
Answer:
y(x)=1x2+3

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user_27qwe
Answered 2021-12-30 Author has 208 answers

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