Use integration to find a general solution of the differential equation. $$\frac { d y } { d x } = x ^ { 10 } e ^ { x ^ { 11 } }$$
A) $y = \frac { 1 } { 10 } e ^ { x ^ { 11 } } + C$
B) $y = \frac { 1 } { 11 } e ^ { x ^ { 11 } } + C$
C) $y = \frac { x ^ { 11 } } { 11 } e ^ { x ^ { 11 } } + C$
D) $y = 11 e ^ { x ^ { 11 } } + C$
E) $y = 10 e ^ { x ^ { 11 } } + C$

Question

Quizplus · Accepted Answer

The integral of $x^{10}e^{x^{11}}$ with respect to $x$ can be found using a substitution method where $u = x^{11}$, thus $du = 11x^{10}dx$. Rearranging for $dx$, we get $dx = \frac{du}{11x^{10}}$. Substituting into the integral, we find that the $x^{10}$ terms cancel out, leaving us with $\frac{1}{11}\int e^u du$, which integrates to $\frac{1}{11}e^{x^{11}} + C$, matching option B.

Use Integration to Find a General Solution of the Differential dydx=x10ex11\frac { d y } { d x } = x ^ { 10 } e ^ { x ^ { 11 } }dxdy​=x10ex11

Use Integration to Find a General Solution of the Differential $\frac { d y } { d x } = x ^ { 10 } e ^ { x ^ { 11 } }$