Solve x² d'y dx² dy + 3x + y = dx 1 (1− x)²
give solution in brief
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Answers
Answered by
3
Answer:
9
−sin3x
+e
x
+
12
x
4
+
3
1
x−1
Step-by-step explanation:
Integrating the given differential equation, we have
dx
dy
=
3
−cos3x
+e
x
+
3
x
3
+C
1
but y
1
(0)=1 so 1=(−1/3)+1+C
1
⇒C
1
=1/3.
Again integrating, we get
y=
9
−sin3x
+e
x
+
12
x
4
+
3
1
x+C
2
but y(0)=0 so 0=0+1+C
2
⇒C
2
=−1.Thus
y=
9
−sin3x
+e
x
+
12
x
4
+
3
1
x−1
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