Which of the following is a solution of the differential equation $\frac { d ^ { 3 } y } { d x ^ { 3 } } - \frac { d ^ { 2 } y } { d x ^ { 2 } } = 0$ that satisfies the initial conditions $y ( 0 ) = - 4$ , $y ^ { \prime } ( 0 ) = - 2$ , $y ^ { \prime \prime } ( 0 ) = - 3$ ?
A) $y = - 1 + x - 3 e ^ { - x }$
B) $y = - 1 + x - 3 e ^ { x }$
C) $y = - 1 + x + 3 e ^ { x }$
D) $y = - 1 + x - 2 e ^ { x }$
E) $y = - 1 - 3 e ^ { x }$
F) $y = 1 + x - 4 e ^ { x }$
G) $y = - 1 + x ^ { 2 } - 3 e ^ { x }$
H)None of these

Question

Which of the following is a solution of the differential equation $\frac { d ^ { 3 } y } { d x ^ { 3 } } - \frac { d ^ { 2 } y } { d x ^ { 2 } } = 0$ that satisfies the initial conditions $y ( 0 ) = - 4$ , $y ^ { \prime } ( 0 ) = - 2$ , $y ^ { \prime \prime } ( 0 ) = - 3$ ?
A) $y = - 1 + x - 3 e ^ { - x }$ 
B) $y = - 1 + x - 3 e ^ { x }$ 
C) $y = - 1 + x + 3 e ^ { x }$ 
D) $y = - 1 + x - 2 e ^ { x }$ 
E) $y = - 1 - 3 e ^ { x }$ 
F) $y = 1 + x - 4 e ^ { x }$ 
G) $y = - 1 + x ^ { 2 } - 3 e ^ { x }$ 
H)None of these

Quizplus · Accepted Answer

The differential equation $\frac { d ^ { 3 } y } { d x ^ { 3 } } - \frac { d ^ { 2 } y } { d x ^ { 2 } } = 0$ has a general solution of the form $y = C_1 + C_2 x + C_3 e^x$. Applying the initial conditions $y(0) = -4$, $y'(0) = -2$, and $y''(0) = -3$ to this form, we find that $C_1 = -1$, $C_2 = 1$, and $C_3 = -3$, leading to the solution $y = -1 + x - 3 e^x$.

Which of the Following Is a Solution of the Differential d3ydx3−d2ydx2=0\frac { d ^ { 3 } y } { d x ^ { 3 } } - \frac { d ^ { 2 } y } { d x ^ { 2 } } = 0dx3d3y​−dx2d2y​=0

Which of the Following Is a Solution of the Differential $\frac { d ^ { 3 } y } { d x ^ { 3 } } - \frac { d ^ { 2 } y } { d x ^ { 2 } } = 0$