Solving Linear Differential Equations of First Order
If yx is the ...
Question
If y(x) is the solution of the differential equation (x+2)dydx=x2+4x–9,x≠–2 and y(0)=0, then y(–4)is equal to :
A
2
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B
0
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C
−1
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D
1
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Solution
The correct option is B0 (x+2)dydx=x2+4x–9dydx=x2+4x–9+4−4x+2dydx=(x+2)2−13x+2∫dy=∫[(x+2)−13x+2]dxy=x22+2x−13ln|(x+2)|+CPutx=0,y=0C=13ln2y=x22+2x−13ln|(x+2)|+13ln2y(−4)=0