APFIVE Particular Solution as a Definite Integral
Let $$y=r(x)$$ be the particular solution to the differential equation $$\frac{dy}{dx}=\frac{1}{\sqrt{1+x^4}}$$ with the initial condition $$r(2)=5$$. Which of the following defines $$r(x)$$?
A
$$r(x)=5+\int_2^x\frac{1}{\sqrt{1+t^4}}\, dt$$
B
$$r(x)=5+\int_0^2\frac{1}{\sqrt{1+t^4}}\, dt$$
C
$$r(x)=\frac{-2x^3}{(1+x^4)^{3/2}}$$
D
$$r(x)=\arctan(x^2)+C$$
Question Leaderboard
| Rank | |||||
|---|---|---|---|---|---|
| #1 | haneesh19.12 | 1 | 1 | 0m 00s | 100 |
| #2 | eftahsam | 1 | 1 | 0m 25s | 75 |
| #3 | npgiahy151108 | 1 | 1 | 1m 16s | 24 |
| #4 | p250001155 | 0 | 1 | 0m 00s | -10 |
| #5 | seojunj | 1 | 2 | 1m 50s | -20 |
Items per page:
10
1 – 5 of 5