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        Solve d^2y/dt + dy/dt = t^2+2t Given that y(0)=4,y'(0)=2
7 years ago

Jitender Singh
IIT Delhi
158 Points
										Ans:$\frac{d^{2}y}{dt^{2}} + \frac{dy}{dt} = t^{2}+2t$$\int d(\frac{dy}{dt}) + \int \frac{dy}{dt} = \int (t^{2}+2t)dt$$(\frac{dy(t)}{dt}) + y(t) = \frac{t^{3}}{3} + t^{2} + c$$(\frac{dy(0)}{dt}) + y(0) = \frac{(0)^{3}}{3} + (0)^{2} + c$$4 + 2 = c$$c = 6$$(\frac{dy(t)}{dt}) + y(t) = \frac{(t)^{3}}{3} + (t)^{2} + 6$$e^{t}(y^{'}(t) + y(t)) = e^{t}(\frac{(t)^{3}}{3} + (t)^{2} + 6)$$\int e^{t}(y^{'}(t) + y(t))dt = \int e^{t}(\frac{(t)^{3}}{3} + (t)^{2} + 6)dt$$\int (e^{t}.y(t))^{'}dt = \int e^{t}(\frac{(t)^{3}}{3} + (t)^{2} + 6)dt$$e^{t}.y(t) = \frac{1}{3}.e^{t}(t^{3}+18) + constant$Thanks & RegardsJitender SinghIIT DelhiaskIITians Faculty

3 years ago
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