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NCERT Class 12 Maths Chapter 9: Differential Equations 23 Questions Solved

NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations — Exercise 9.3

Click any question below for its step-by-step NCERT textbook solution, concept hints, and worked explanation.

Solve y′=(1−cos x)/(1+cos x).

Solve y′=√(4−y²), −2<y<2.

Solve y′+y=1, y≠1.

Solve sec²x tan y dx+sec²y tan x dy=0.

Solve (eˣ+e^(−x))dy−(eˣ−e^(−x))dx=0.

Solve y′=(1+x²)(1+y²).

Solve y log y dx−x dy=0.

Solve x⁵y′=−y⁵.

Solve y′=sin⁻¹x.

Solve eˣtan y dx+(1−eˣ)sec²y dy=0.

Solve (x³+x²+x+1)y′=2x²+x, y(0)=1.

Solve x(x²−1)y′=1, y(2)=0.

Solve cos(y′)=a, a∈R, with y(0)=1.

Solve y′=y tan x, y(0)=1.

Find the curve through (0,0) with y′=eˣ sin x.

Solve xy y′=(x+2)(y+2), passing through (1,−1).

Find the curve through (0,−2) where y times the tangent slope equals x.

The tangent slope is twice the slope from (−4,−3) to (x,y). Find the curve through (−2,1).

A spherical balloon volume increases at a constant rate. Its radius is 3 initially and 6 after 3 s. Find radius at t seconds.

Continuous growth at r%/year doubles ₹100 in 10 years. Find r, using log 2=0.6931.

₹1000 grows continuously at 5%/year. Find its value after 10 years using e^0.5=1.648.

A culture starts with 100000 bacteria and grows by 10% in 2 h, at a rate proportional to population. When does it reach 200000?

Choose the general solution of y′=e^(x+y).