(a) Show that every member of the family of functions $y = c e ^ { \frac { 1 } { 3 } x ^ { 3 } }$ is a solution of the differential equation $y ^ { \prime } = x ^ { 2 } y$ .(b) Find a solution of the differential equation $y ^ { \prime } = x ^ { 2 } y$ that satisfies the initial condition $y ( 0 ) = 8$ .(c) Find a solution of the differential equation $y ^ { \prime } = x ^ { 2 } y$ that satisfies the initial condition $y ( 8 ) = 0$ .

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The Answer of (a) Show that every member of the family of functions $y = c e ^ { \frac { 1 } { 3 } x ^ { 3 } }$ is a solution of the differential equation $y ^ { \prime } = x ^ { 2 } y$ .(b) Find a solution of the differential equation $y ^ { \prime } = x ^ { 2 } y$ that satisfies the initial condition $y ( 0 ) = 8$ .(c) Find a solution of the differential equation $y ^ { \prime } = x ^ { 2 } y$ that satisfies the initial condition $y ( 8 ) = 0$ .

(A) Show That Every Member of the Family of Functions y=ce13x3y = c e ^ { \frac { 1 } { 3 } x ^ { 3 } }y=ce31​x3

(A) Show That Every Member of the Family of Functions $y = c e ^ { \frac { 1 } { 3 } x ^ { 3 } }$