Q9 of 118 Page 395

For each of the differential equations in question, find the general solution:

Separating variables,

Integrating both sides,

Now to integrate we have to multiply it by 1
because,

∵ { - i)

So,

According to i)

Let u be and v be 1

We can take the values of u and v from the formula (I.L.A.T.E)

So,

putting the value of t,

For each of the differential equations in question, find the general solution:

y log y dx – x dy = 0

For each of the differential equations in question, find the general solution:

e^xtan y dx + 1(1 – e^x)sec²y dy = 0

For each of the differential equations in question, find a particular solution satisfying the given condition:

(x³ + x² + x + 1) dy/dx = 2x² + x, y = 1 when x = 0