Motions and ODE

Calculus Level 1

For a body moving along a straight line, let y ( t ) y(t) denote its distance from a fixed point O O at time t . t. Given that velocity plus distance is equal to square of time, find the ordinary differential equation of the motion.

y + t y = t 2 {y}^{\prime\prime}+ty={t}^{2} t y + y = t 2 {ty}^{\prime}+y={t}^{2} y + y = t 2 {y}^{\prime\prime}+y={t}^{2} y + y = t 2 {y}^{\prime}+y={t}^{2}

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