AP EAMCET · Maths · Differential Equations
The substitution \(\frac{d y}{d x}=z\), reduces the differential equation \(\frac{d^2 y}{d x^2}-\frac{d y}{d x}=0\) to a differential equation whose solution is \(\mathrm{z}=\)
- A \(\log \mathrm{x}+\mathrm{C}\)
- B \(\mathrm{x}+\mathrm{C}\)
- C \(\mathrm{Ae}^{\mathrm{X}}\)
- D \(\mathrm{x}^2+\mathrm{C}\)
Answer & Solution
Correct Answer
(C) \(\mathrm{Ae}^{\mathrm{X}}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { Here, } \frac{\mathrm{dy}}{\mathrm{dx}}=\mathrm{z} \Rightarrow \frac{\mathrm{d}^2 \mathrm{y}}{\mathrm{dx}^2}=\frac{\mathrm{dz}}{\mathrm{dx}} \\ & \Rightarrow \frac{\mathrm{dz}}{\mathrm{dx}}-\mathrm{z}=0 \Rightarrow…
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