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Find the value of kk for which the constant function x(t)=kx(t)=k is a solution of the differential equation 3t3dxdt+5x−3=03t3dxdt+5x−3=0.

Find the value of kk for which the constant function x(t)=kx(t)=k is a solution of the differential equation 3t3dxdt+5x−3=03t3dxdt+5x−3=0.
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Find the value of kk for which the constant function x(t)=kx(t)=k is a solution of the differential equation 3t3dxdt+5x−3=03t3dxdt+5x−3=0.

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User Swaraj Giri
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1 Answer

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If
x(t)=k is constant, then
(\mathrm dx)/(\mathrm dt)=0, so you have


5k-3=0\implies k=\frac35
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User Jazimov
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