Solve the following ivp:

2. 2x^2 +y^2 +xyy′ =0, x> 0, y(1)=1

Step-by-step explanation:

The given differential equation is:

We rewrite this as

We make the subject to get:

....a homogeneous equation.

We use the following substitutions to obtain a seperable equation:

.

This implies that:

We integrate both sides to obtain:

We substitute to get:

We substitute x=1,y=1 from the initial conditions.

Our solution now becomes:

29.5977692753

step-by-step explanation:

(f - g)(x) = 5x^3 - 3

step-by-step explanation:

rearrange these functions vertically, with like terms in separate columns:

f(x) = 5x^3 - 2

g(x) =         +1

now subtract, column by column:

(f - g)(x) = 5x^3 - 3