Which of the following functions solves the differential equation: $y ^ { \prime } = e ^ { - 2 x } + 3 ?$
A) y = $e ^ { - 2 x }$ + 3
B) y = $\frac { 1 } { 2 }$ $e ^ { - 2 x }$ + 3
C) y = - $\frac { 1 } { 2 }$ $e ^ { - 2 x }$ + 3x
D) none of these

Question

Quizplus · Accepted Answer

The correct solution is found by integrating the right-hand side of the differential equation $y' = e^{-2x} + 3$. Integrating $e^{-2x}$ gives $-\frac{1}{2}e^{-2x}$, and integrating 3 with respect to x gives $3x$. Therefore, the solution is $y = -\frac{1}{2}e^{-2x} + 3x + C$, where C is the constant of integration. Since the constant C is not specified, the closest match is option C, $y = -\frac{1}{2}e^{-2x} + 3x$, assuming C=0.

Which of the Following Functions Solves the Differential Equation y′=e−2x+3?y ^ { \prime } = e ^ { - 2 x } + 3 ?y′=e−2x+3?

Which of the Following Functions Solves the Differential Equation $y ^ { \prime } = e ^ { - 2 x } + 3 ?$