Verify: $x^2+y^2=r^2$, and $x\dfrac{dy}{dx}+r\sqrt{1+\left(\dfrac{dy}{dx}\right)^2}=y$

Verify: x²+y²=r², and x(dy)/(dx)+r√(1+((dy)/(dx))²)=y

Miscellaneous Exercise 6(II) · Q116

x^2+y^2=r^2

Maharashtra MsbshseTextbookSubjectiveImportance★★★★★est

66% · 116/177 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 →

$x^2+y^2=r^2$ (implicit): differentiate, $2x+2y\dfrac{dy}{dx}=0\Rightarrow\dfrac{dy}{dx}=-\dfrac{x}{y}$ . Check the claim: $x\dfrac{dy}{dx}+r\sqrt{1+\left(\dfrac{dy}{dx}\right)^2}=x\left(-\dfrac{x}{y}\right)+r\sqrt{1+\dfrac{x^2}{y^2}}=-\dfrac{x^2}{y}+r\cdot\dfrac{\sqrt{x^2+y^2}}{y}=-\dfrac{x^2}{y}+\dfrac{r^2}{y}=\dfrac{r^2-x^2}{y}= …

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

←Previous questionQ115 — Determine the order and degree: (d⁴y)/(dx⁴)+sin((dy)/(dx))=0 →Next questionQ117 — Verify: y=eaxsin bx, and (d²y)/(dx²)-2a(dy)/(dx)+(a²+b²)y=0

Q.Verify: $x^2+y^2=r^2$ , and $x\dfrac{dy}{dx}+r\sqrt{1+\left(\dfrac{dy}{dx}\right)^2}=y$

Concept understanding — General and Particular Solutions of a Differential Equation

Q.Verify: x2+y2=r2x^2+y^2=r^2x2+y2=r2, and xdydx+r1+(dydx)2=yx\dfrac{dy}{dx}+r\sqrt{1+\left(\dfrac{dy}{dx}\right)^2}=yxdxdy​+r1+(dxdy​)2​=y

🎓Unlock everything free for 14 days

Q.Verify: $x^2+y^2=r^2$ , and $x\dfrac{dy}{dx}+r\sqrt{1+\left(\dfrac{dy}{dx}\right)^2}=y$

Unlock everything free for 14 days