Solve the problem $y ^ { \prime } = ( x + 1 ) y , y ( 0 ) = 1$ numerically for $y ( 0.2 )$ using $h = 0.1$ .
A) 1.1
B) 1.11
C) 1.2
D) 1.21
E) 1.221

Question

Quizplus · Accepted Answer

Using Euler's method with step size $h = 0.1$, we approximate $y(0.2)$ by first calculating $y(0.1)$ and then $y(0.2)$. Starting with $y(0) = 1$, we find $y(0.1) \approx 1 + 0.1 \times (0 + 1) \times 1 = 1.1$. Then, $y(0.2) \approx 1.1 + 0.1 \times (0.1 + 1) \times 1.1 = 1.221$.

Solve the Problem y′=(x+1)y,y(0)=1y ^ { \prime } = ( x + 1 ) y , y ( 0 ) = 1y′=(x+1)y,y(0)=1

Solve the Problem $y ^ { \prime } = ( x + 1 ) y , y ( 0 ) = 1$