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

Question

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

Quizplus · Accepted Answer

This is a first-order linear differential equation. The integrating factor is $e^t$, and after applying it, the solution to the differential equation is $y = Ce^t - 1$. Using the initial condition $y(0) = 1$, we find $C = 2$, so the solution is $y = 2e^t - 1$.

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

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