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the d.e whose solution is y=ax2)+(b)/(x) is
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The D.E whose solution is y=ax2+bx is:

y2​x2−2xy1​+2y=0

Solution

y=ax2+bx
⇒y1​=2ax+b
⇒y2​=2a
⇒b=y1​−y2​x
→y=ax2+bx
⇒y=2y2​​x2+(y1​−y2x​)x
y=2y2​​x2+y1​x−y2​x2
⇒y=22y1​x−y2​x2​

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