Solve the differential equation with the given initial condition.
-$y ^ { \prime } = t y , y ( 0 ) = - 1$
A) y = $e ^ { t + 1 }$
B) y = - $\mathrm { e } t^ { 2 } / 2$
C) y = $\frac { t ^ { 2 } } { 2 }$
D) y = -1 + $\mathrm { e } t^ { 2 } / 2$

Question

Solve the differential equation with the given initial condition. 
-$y ^ { \prime } = t y , y ( 0 ) = - 1$
A) y = $e ^ { t + 1 }$
B) y = - $\mathrm { e } t^ { 2 } / 2$
C) y = $\frac { t ^ { 2 } } { 2 }$
D) y = -1 + $\mathrm { e } t^ { 2 } / 2$

Quizplus · Accepted Answer

This is a first-order linear differential equation. The solution can be found using the method of separation of variables. Integrating both sides gives $y = -e^{t^2/2} + C$. Using the initial condition $y(0) = -1$, we find $C = 0$, so the solution is $y = -e^{t^2/2}$.

Solve the Differential Equation with the Given Initial Condition y′=ty,y(0)=−1y ^ { \prime } = t y , y ( 0 ) = - 1y′=ty,y(0)=−1

Solve the Differential Equation with the Given Initial Condition $y ^ { \prime } = t y , y ( 0 ) = - 1$