Differential EquationseasyFree

Order of DE for y=c₁cos2x+c₂cos²x+c₃sin²x+c₄ | JEE

JEE Maths question with a full step-by-step solution.

Question
The order of the differential equation corresponding to y=c1cos⁡2x+c2cos⁡2x+c3sin⁡2x+c4y = c_1\cos 2x + c_2\cos^2 x + c_3\sin^2 x + c_4 is:
A22correct
B44
C33
D11
Solution
Use cos⁡2x=1+cos⁡2x2\cos^2 x = \dfrac{1+\cos 2x}{2} and sin⁡2x=1−cos⁡2x2\sin^2 x = \dfrac{1-\cos 2x}{2}:
y=c1cos⁡2x+c22(1+cos⁡2x)+c32(1−cos⁡2x)+c4.y = c_1\cos 2x + \frac{c_2}{2}(1+\cos 2x) + \frac{c_3}{2}(1-\cos 2x) + c_4.
 Collect the constant and the cos⁡2x\cos 2x terms:
y=(c22+c32+c4)+(c1+c22−c32)cos⁡2x=A+Bcos⁡2x.y = \left(\frac{c_2}{2}+\frac{c_3}{2}+c_4\right) + \left(c_1 + \frac{c_2}{2} - \frac{c_3}{2}\right)\cos 2x = A + B\cos 2x.
 ⇒\Rightarrow only two independent arbitrary constants A,BA, B survive, so the order is 22. Correct answer: (1)
Still stuck on this question?Ask your doubt on WhatsApp
Similar questions
Differential Equations · easy
The differential equation of all parabolas with axis parallel to the yy-axis is:
Differential Equations · easy
Let x dydx−y=x2(xex+ex−1)\dfrac{x\,dy}{dx} - y = x^2(xe^x + e^x - 1) for all x∈R−{0}x \in R - \{0\} with y(1)=e−1y(1) = e - 1. If y(2)=k y(1)(y(1)+2)y(2) = k\,y(1)\big(y(1)+2\big), then the value of kk is:
Differential Equations · easy
The equation dydx=x2+y2+12xy\dfrac{dy}{dx} = \dfrac{x^2 + y^2 + 1}{2xy}, with y(1)=1y(1) = 1, is the differential equation of:
Differential Equations · easy
The differential equation ey dx+(eyx+2y) dy=0e^y\,dx + (e^y x + 2y)\,dy = 0 has the particular solution y(0)=1y(0) = 1. The value of xx when y=0y = 0 is:

Solve more, learn faster

Sign up free to solve more JEE Maths questions and explore doMath — timed drills, mastery sprints, bookmarks, and chapter-wise progress tracking.

Sign up freeExplore doMath