Solve the initial value problem d y / d x = 8 ( x 3 ) ∗ e − 2 y y(1)=0

Question

Solve the initial value problem  d  y      /    d  x  =  8  (      x          3        )  ∗      e          −      2      y      y(1)=0

Kaiden Weeks · Accepted Answer

d      y              d      x        =  8      x          3            e          −      2      y        ⇒      e          2      y        d  y  =  8      x          3        d  x  ∫      e          2      y        d  y  =  ∫  8      x          3        d  x      1    2        e          2      y        =  2      x          4        +  Cy(1)=0  ⇒      1    2        e          2      ∗      0        =  2  ∗  (  1      )          4        +  C  ⇒      1    2    =  2  +  C  ,  C  =  −      3    2        1    2        e          2      y        =  2      x          4        −      3    2        e          2      y        =  4      x          4        −  3  2  y  =  ln  ⁡  (  4      x          4        −  3  )  y  =      1    2    ln  ⁡  (  4      x          4        −  3  )

Ethen Blackwell · Accepted Answer

∫      e          2      y        d  y  =  8  ∫      x          3        d  x      1    2        e          2      y        =  2      x          4        +  c  y  =      1    2    ln  ⁡  (  4      x          4        +  A  )for the initial value y(1)=0 ie. y = 0, x = 1,  0  =  0.5  ln  ⁡  (  4  +  A  )  ln  ⁡  (  4  +  A  )  =  0      e          0        =  1  =  4  +  A  ∴  A  =  −  3thus the solution is:  y  =      1    2    ln  ⁡  (  4      x          3        −  4  )

Solve the initial value problem dy/dx=8(x^3)*e^(-2y) y(1)=0

Answered question

Answer & Explanation

New Questions in Calculus 1