Use a computer algebra system (CAS) to solve the given initial value problem.
-$$y ^ { \prime } = \frac { 2 \left( 1 - x ^ { 2 } \right) } { 1 + x ^ { 2 } } , y ( 0 ) = 1$$
A) $y = 4 \tan ^ { - 1 } x - 2 x$
B) $y = 2 \ln \left( \frac { x + 1 } { | x - 1 | } \right) - 2 x + 1$
C) $y = 3 \tan ^ { - 1 } x - x + 1$
D) $y = 4 \tan ^ { - 1 } x - 2 x + 1$

Question

Quizplus · Accepted Answer

To solve the given initial value problem, we integrate the given differential equation $y' = \frac{2(1-x^2)}{1+x^2}$ to find $y$. The integral of the right-hand side with respect to $x$ gives $y = 4\tan^{-1}x - 2x + C$. Using the initial condition $y(0) = 1$, we find that $C = 1$, leading to the solution $y = 4\tan^{-1}x - 2x + 1$.

Use a Computer Algebra System (CAS) to Solve the Given y′=2(1−x2)1+x2,y(0)=1y ^ { \prime } = \frac { 2 \left( 1 - x ^ { 2 } \right) } { 1 + x ^ { 2 } } , y ( 0 ) = 1y′=1+x22(1−x2)​,y(0)=1

Use a Computer Algebra System (CAS) to Solve the Given $y ^ { \prime } = \frac { 2 \left( 1 - x ^ { 2 } \right) } { 1 + x ^ { 2 } } , y ( 0 ) = 1$