Question
Solve the following differential equation:
(1/y²) (dy/dt) = 1 - e⁻³ᵗ
(c) Show that the equation
(y - 2x³)dx = x(1 - xy)dy
becomes exact on multiplication by x⁻² and solve it.
Answer :
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Skip in 10
For the first differential equation, ((1/y^2)(dy/dt) = 1 - e^{-3t}), multiply both sides by (y^2) to get (\frac{dy}{dt} = y^2 (1 - e^{-3t})). This is separable: (\frac{dy}{y^2} = (1 - e^{-3t}) dt). Integrating both sides gives (-1/y = t
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