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NCERT Class 12 Maths Chapter 9: Differential Equations 15 Questions Solved

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

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

Give order and degree: (i) y″+5x(y′)²−6y=log x; (ii) (y′)³−4(y′)²+7y=sin x; (iii) y⁽⁴⁾−sin(y‴)=0.

Verify (i) xy=aeˣ+be^(−x)+x² solves xy″+2y′−xy+x²−2=0; (ii) y=eˣ(a cos x+b sin x) solves y″−2y′+2y=0; (iii) y=x sin 3x solves…

Prove x²−y²=c(x²+y²)² solves (x³−3xy²)dx=(y³−3x²y)dy.

Solve y′+√[(1−y²)/(1−x²)]=0.

Show y′+(y²+y+1)/(x²+x+1)=0 has family x+y+1=A(1−x−y−2xy).

Find the curve through (0,π/4) for sin x cos y dx+cos x sin y dy=0.

Solve (1+e^(2x))dy+(1+y²)eˣdx=0, y(0)=1.

Solve y e^(x/y)dx=[x e^(x/y)+y²]dy, y≠0.

Solve (x−y)(dx+dy)=dx−dy, y(0)=−1.

Solve [e^(−2√x)/√x−y/√x] dx/dy=1, x≠0. The real equation requires x>0.

Solve y′+\(\cot{\left(x \right)}\) y=\(4 x \csc{\left(x \right)}\). Given y(\(\frac{\pi}{2}\))=\(0\).

Solve (x+1)y′=2e^(−y)−1 with y(0)=0.

Choose the general solution of (y dx−x dy)/y=0.

Choose the general solution of dx/dy+P₁(y)x=Q₁(y).

Choose the general solution of eˣdy+(yeˣ+2x)dx=0.