x² d²y/dx²-2x(1+x) dy/dx +(1+x)y=x³ solve differential equation
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Answered by
1
Answer:
On dividing the given equation by x^2, it becomes y'' - 2[(1+x)/x]y' + 2(1+x)y/x^2 = x, which is a second order linear differential equation
Answered by
7
Answer:
Differential equation (1+x
2
)
dx
dy
+2xy=4x
2
dx
dy
+
1+x
2
2x
y=
1+x
2
4x
2
It is a linear differential equation
dx
dy
+Py=Q where P=
1+x
2
2x
Q=
1+x
2
4x
2
I.F. =e
∫Pdx
I. F. =e
∫
1+x
2
2x
dx
1+x
2
=t
2xdx=dt
I.F.=e
∫
t
dt
I.F.=e
log
e
t
I.F.=t=(1+x
2
)
y(I.F)=∫(I.F.)Qdx+c
y(1+x
2
)=∫
1+x
2
4x
2
(1+x
2
)dx+c
y(1+x
2
)=∫4x
2
dx+c
y(1+x
2
)=4∫x
2
dx+c
y(1+x
2
)=4(
3
x
3
)+c
y(1+x
2
)=
3
4
(x
3
)+c.
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