FIRST ORDER VARIABLE SEPARABLE DIFFERENTIAL EQUATIONS 

Solved Problems

Problem 1-6 : Solve the given first order differentiable equation by variable separable.

Problem 1 :

Solution :

Integrate both sides.

Problem 2 :

3e^xtanydx + (1 + e^x)sec²ydy = 0

Solution :

3e^xtanydx + (1 + e^x)sec²ydy = 0

(1 + e^x)sec²ydy = -3e^xtanydx

ln(tany) = -3ln(1 + e^x) + ln(c)

ln(tany) + 3ln(1 + e^x) = ln(c)

ln(tany) + ln(1 + e^x)³ = ln(c)

ln[tany(1 + e^x)³] = ln(c)

(1 + e^x)³tany = c

Problem 3 :

Solution :

Problem 4 :

Solution :

Let t = 1 - y².

Here, u = x and dv = e^xdx.

(1)---->

Problem 5 :

Solution :

Let x + y = z.

Differentiate with respect to x.

Then, the given differential eq

Problem 6 :

Solution :

Let t = x⁴.

Differentiate with respect to x.

(1)---->

Problem 7 :

Solve (x² - y)dx + (y² - x)dy = 0, if it passes through the origin.

Solution :

(x² - y)dx + (y² - x)dy = 0

x²dx - ydx + y²dy- xdy = 0

x²dx + y²dy = xdy + ydx

x²dx + y²dy = d(xy)

Integrate both sides.

Since it passes through origin, x = 0 and y = 0.

0 + 0 = 0 + c

c = 0

Therefore, the required solution is

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.