Given the differential equation with the given initial condition: $y ^ { \prime } = \sqrt { \frac { t + 1 } { y } } ; y ( 0 ) = 4$ is this the solution $y = \left( ( t + 1 ) ^ { 3 / 2 } + 4 \right) ^ { 2 / 3 } \text { ? }$

Question

Quizplus · Accepted Answer

The given solution does not satisfy the initial condition $y(0) = 4$, as plugging $t = 0$ into the solution does not yield $y = 4$.

Given the Differential Equation with the Given Initial Condition y′=t+1y;y(0)=4y ^ { \prime } = \sqrt { \frac { t + 1 } { y } } ; y ( 0 ) = 4y′=yt+1​​;y(0)=4

Given the Differential Equation with the Given Initial Condition $y ^ { \prime } = \sqrt { \frac { t + 1 } { y } } ; y ( 0 ) = 4$