For each of the following initial value problems verify that the accompanying function is a solution: Function: Two mathematical expressions are provided: the differential equation dy/dx = y with initial condition y(0) = 1, and the function y = e^x.

Q2 of 462 Page 22

For each of the following initial value problems verify that the accompanying function is a solution:

Function:

Verification:

Differentiating both sides we get,

Since y=e^x , we can replace e^x in the above differential equation

Hence y = e^x is the solution of the differential equation.

Also, at x=0, we get y=e⁰ which is equal to 1.

For each of the following differential equations verify that the accompanying function is a solution.

Differential equation

ii.

iii.

iv.

Function

For each of the following initial value problems verify that the accompanying function is a solution:

Function: y = log x

For each of the following initial value problems verify that the accompanying function is a solution:

Function: y=sin x

For each of the following initial value problems verify that the accompanying function is a solution:

Function: y=e^x+1