Two solutions to y'' – 2y' – 35y = 0 are yı = e, y2 = e -5t a) find the wronskian. w = 0 preview b) find the solution satisfying the initial conditions y(0) = – 7, y'(0) = 23 y = ( preview

a.

b.

Step-by-step explanation:

We have a differential equation

y''-2 y'-35 y=0

Auxillary equation

By factorization method we are  finding the solution

Substitute each factor equal to zero

D-7=0  and D+5=0

D=7  and D=-5

Therefore ,

General solution is

Let

We have to find Wronskian

Substitute values then we get

a.

We are given that y(0)=-7 and y'(0)=23

Substitute the value in general solution the we get

....(equation I)

......(equation II)

Equation I is multiply by 5 then we subtract equation II from equation I

Using elimination method we eliminate

Then we get

Substitute the value of in  I equation then we get

Hence, the general solution is

b.

there are many solutions.

step-by-step explanation:

step 1: simplify both sides of the equation.

4x+6=4x^2+10x−4

step 2: subtract 4x^2+10x-4 from both sides.

4x+6−(4x^2+10x−4)=4x^2+10x−4−(4x^2+10x−4)

−4x^2−6x+10=0

step 3: factor left side of equation.

−2(2x+5)(x−1)=0

step 4: set factors equal to 0.

x=-5/2 or x=1

a

step-by-step explanation: