The D- E is d 3 y d x 3 1 6 - d y d x 1 3 -5 Prove that- d 3 y d x 3 - d y d x 2 -5 6

Given, ( d^2ydx^3 )^16· ( dydx )^13=5 cubing on both sides, we get, ( d^2ydx^3 )^36· ( dydx )^33=5^3 ( d^2ydx^3 )^12· ( dydx )=5^3 squaring on both ...

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Byju's Answer

Standard XII

Mathematics

Differential Equations Definition

The D· E is...

Question

The $D \cdot E$ is ${(\frac{d^{3} y}{d x^{3}})}^{\frac{1}{6}} \cdot {(\frac{d y}{d x})}^{\frac{1}{3}} = 5$
Prove that: $(\frac{d^{3} y}{d x^{3}}) \cdot {(\frac{d y}{d x})}^{2} = 5^{6}$

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Solution

Given,

${(\frac{d^{2} y}{d x^{3}})}^{\frac{1}{6}} \cdot {(\frac{d y}{d x})}^{\frac{1}{3}} = 5$

cubing on both sides, we get,

${(\frac{d^{2} y}{d x^{3}})}^{\frac{3}{6}} \cdot {(\frac{d y}{d x})}^{\frac{3}{3}} = 5^{3}$

${(\frac{d^{2} y}{d x^{3}})}^{\frac{1}{2}} \cdot (\frac{d y}{d x}) = 5^{3}$

squaring on both sides, we get,

${(\frac{d^{2} y}{d x^{3}})}^{\frac{2}{2}} \cdot {(\frac{d y}{d x})}^{2} = (5^{3})^{2}$

$(\frac{d^{2} y}{d x^{3}}) \cdot {(\frac{d y}{d x})}^{2} = 5^{6}$

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The D⋅E is (d3ydx3)16⋅(dydx)13=5 Prove that: (d3ydx3)⋅(dydx)2=56

Given,(d2ydx3)16⋅(dydx)13=5cubing on both sides, we get,(d2ydx3)36⋅(dydx)33=53(d2ydx3)12⋅(dydx)=53squaring on both sides, we get,(d2ydx3)22⋅(dydx)2=(53)2(d2ydx3)⋅(dydx)2=56

The $D \cdot E$ is ${(\frac{d^{3} y}{d x^{3}})}^{\frac{1}{6}} \cdot {(\frac{d y}{d x})}^{\frac{1}{3}} = 5$
Prove that: $(\frac{d^{3} y}{d x^{3}}) \cdot {(\frac{d y}{d x})}^{2} = 5^{6}$