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The differential equation representing family of curves y = aemx + benx, where a and b are arbitrary constants, is |
\(\frac{d^2y}{dx^2}\)+(m + n)\(\frac{dy}{dx}\) + y =0 \(\frac{d^2y}{dx^2}\)+(mn)\(\frac{dy}{dx}\) +(m + n) y =0 \(\frac{d^2y}{dx^2}\)-(m + n)\(\frac{dy}{dx}\) + mny =0 \(\frac{d^2y}{dx^2}\)+(m + n)\(\frac{dy}{dx}\) - mny =0 |
\(\frac{d^2y}{dx^2}\)-(m + n)\(\frac{dy}{dx}\) + mny =0 |
y = aemx + benx on differentiating both side, we get $\frac{dy}{dx}=ame^{mx}+bne^{nx}$ Again differentiating, we get $\frac{d^2y}{dx^2}=am^2e^{mx}+bn^2e^{nx}$ $∴\frac{d^2y}{dx^2}-(m+n)\frac{dy}{dx}+mny=am^2e^{mx}+bn^2e^{nx}$ $-(m+n)[ame^{mx}+bne^{nx}]+mn[ae^{mx}+be^{nx}]$ $=0$ |
