Determine the order and degree (if defined) of: d^4y/dx^4 + sin(y''') = 0.
Hint. Identify the highest derivative present, then check whether the equation is a polynomial in that derivative.
The highest order derivative present is d^4y/dx^4, so the order is 4. Since the equation involves sin(y'''), it is not a polynomial equation in its derivatives, so the degree is not defined.
✦ Order 4, degree not defined
Determine the order and degree (if defined) of: y'+5y=0.
Hint. Identify the highest derivative present, then check the power it is raised to.
The highest order derivative present is y', so the order is 1. The equation is a polynomial in y' with the highest power raised to 1, so the degree is 1.
✦ Order 1, degree 1
Determine the order and degree (if defined) of: (ds/dt)^4 + 3s(d^2s/dt^2) = 0.
Hint. Identify the highest derivative present, then check the power it is raised to.
The highest order derivative present is d^2s/dt^2, so the order is 2. Since the highest power raised to d^2s/dt^2 is 1, the degree is 1.
✦ Order 2, degree 1
Determine the order and degree (if defined) of: (d^2y/dx^2)^2 + cos(dy/dx) = 0.
Hint. Identify the highest derivative present, then check whether the equation is a polynomial in that derivative.
The highest order derivative present is d^2y/dx^2, so the order is 2. Since the equation involves cos(dy/dx), a non-polynomial function of a lower derivative, it is not a polynomial equation in its derivatives, so the degree is not defined.
✦ Order 2, degree not defined
Determine the order and degree (if defined) of: d^2y/dx^2 = cos3x+sin3x.
Hint. Identify the highest derivative present, then check the power it is raised to.
Since d^2y/dx^2 is the highest order derivative present, the order is 2; because it is raised to the power 1, the degree is also 1.
✦ Order 2, degree 1
Determine the order and degree (if defined) of: (y''')^2 + (y'')^3 + (y')^4 + y^5 = 0.
Hint. Identify the highest derivative present, then check the power it is raised to.
The highest order derivative present is y''', so the order is 3. Since the highest power raised to y''' is 2, the degree is 2.
✦ Order 3, degree 2
Determine the order and degree (if defined) of: y'''+2y''+y'=0.
Hint. Identify the highest derivative present, then check the power it is raised to.
Since y''' is the highest order derivative present, the order is 3; because it is raised to the power 1, the degree is also 1.
✦ Order 3, degree 1
Determine the order and degree (if defined) of: y'+y=e^x.
Hint. Identify the highest derivative present, then check the power it is raised to.
Since y' is the highest order derivative present, the order is 1; because it is raised to the power 1, the degree is also 1.
✦ Order 1, degree 1
Determine the order and degree (if defined) of: y''+(y')^2+2y=0.
Hint. Identify the highest derivative present, then check the power it is raised to.
The highest order derivative present is y'', so the order is 2. Since the highest power raised to y'' is 1, the degree is 1.
✦ Order 2, degree 1
Determine the order and degree (if defined) of: y''+2y'+sin y=0.
Hint. Identify the highest derivative present, then check whether the equation is a polynomial in that derivative.
Since y'' is the highest order derivative present, the order is 2; because sin y is a function of y itself (not of a derivative), the equation is still polynomial in its derivatives, so the degree is 1.
✦ Order 2, degree 1
Choose the correct answer: the degree of the differential equation (d^2y/dx^2)^3 + (dy/dx)^2 + sin(dy/dx) + 1 = 0 is (A) 3 (B) 2 (C) 1 (D) not defined
Hint. Check whether the equation is a polynomial in its highest derivative before reading off a power.
Since the equation involves sin(dy/dx), a non-polynomial function of a derivative (even though it is not the highest-order one), the whole equation is not a polynomial equation in its derivatives, so the degree is not defined.
✦ (D) not defined
Choose the correct answer: the order of the differential equation 2x^2(d^2y/dx^2)-3(dy/dx)+y=0 is (A) 2 (B) 1 (C) 0 (D) not defined
Hint. Identify the highest derivative present in the equation.
Because d^2y/dx^2 is the highest order derivative present in this equation, and no other consideration affects order, the order is simply 2.
✦ (A) 2
Solutions written by the tuition.in editorial team and checked against lemh203.pdf (NCERT, Reprint 2026-27). Questions are referenced from the NCERT textbook for identification.
Pair self-study with a tutor, a live course or a coaching centre.
