Question

steps and answer of dy/dx-y=5.2

Answer 1

Equation at the end of step 1 :

y 26
(((d • —) • x) - y) - —— = 0
d 5
Step 2 :

y
Simplify —
d
Equation at the end of step 2 :

y 26
(((d • —) • x) - y) - —— = 0
d 5
Step 3 :Subtracting a fraction from a whole

Rewrite the whole as a fraction using 5 as the denominator :

yx - y (yx - y) • 5
yx - y = —————— = ————————————
1 5
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Step 4 :

Pulling out like terms :

4.1 Pull out like factors :

yx - y = y • (x - 1)

Adding fractions that have a common denominator :

4.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

y • (x-1) • 5 - (26) 5yx - 5y - 26
———————————————————— = —————————————
5 5
Equation at the end of step 4 :

5yx - 5y - 26
————————————— = 0
5
Step 5 :

When a fraction equals zero :

5.1 When a fraction equals zero ...
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

5yx-5y-26
————————— • 5 = 0 • 5
5
Now, on the left hand side, the 5 cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :
5yx-5y-26 = 0

Solving a Single Variable Equation :

5.2 Solve 5yx-5y-26 = 0

Answer 2

Final result : |y+5.2| =Ce^x.

If y > -5.2 , then y = Ce^x-5.2

If y<-5.2, then y = -Ce^x-5.2.
where C is arbitrary constant .
Steps:
1) This is a separable differential equation.
so, y terms in side of dy .

2)Integrate both sides.
For Calulation process,
see attach file.
Hope, you understand my answer!