Obtain the differential equation by eliminating the arbitrary constants: y=c₁e3x+c₂e2x

Exercise 6.2 · Q16

y=c_1e^{3x}+c_2e^{2x}

Maharashtra MsbshseTextbookSubjectiveImportance★★★★★

9% · 16/177 Questions

🔒 Locked · start free trial →

You're viewing a preview — the full solution, concept, methods & PYQ mapping are locked.

Start your 14-day free trial to unlock the full solution →

$y=c_1e^{3x}+c_2e^{2x}$ has two arbitrary constants, with characteristic roots $3$ and $2$ , so it solves $\dfrac{d^2y}{dx^2}-(3+2)\dfrac{dy}{dx}+(3)(2)y=0$ . Checking directly: $\dfrac{dy}{dx}=3c_1e^{3x}+2c_2e^{2x}$ , $\dfrac{d^2y}{dx^2}=9c_1e^{3x}+4c_2e^{2x}$ . Using the three equations in $c_1e^{3x},c_2e^{2x}$ (as in the chapter …

Start your 14-day free trial to unlock the full solution →

←Previous question · 6.2Q15 — Obtain the differential equation by eliminating the arbitrary constant…→Next question · 6.2Q17 — Obtain the differential equation by eliminating the arbitrary constant…

Q.Obtain the differential equation by eliminating the arbitrary constants: $y=c_1e^{3x}+c_2e^{2x}$

Concept understanding — Formation of a Differential Equation whose General Solution is Given

Q.Obtain the differential equation by eliminating the arbitrary constants: y=c1e3x+c2e2xy=c_1e^{3x}+c_2e^{2x}y=c1​e3x+c2​e2x

🎓Unlock everything free for 14 days

Q.Obtain the differential equation by eliminating the arbitrary constants: $y=c_1e^{3x}+c_2e^{2x}$

Unlock everything free for 14 days