- **Differential Equations**
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- - **Differential Equations**
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Differential Equations1 Attachment(s) I have attached the question images Q43 & Q44. These are my previous year questions, which I was unable to solve. Kindly help me. Thank you |

Why don't you just plug the different solutions into the equation and see whether you get a correct result? |

That's certainly the most direct approach. I think that the first question has an error. None of them look like solutions. I suspect the second also has an error, but it does at least have a solution. |

Quote:
But I'm not sure what else needs to be done to derive one of the solutions given. Q44. I have substituted the solutions in the D.E and I'm getting option A & B as solutions. Is it correct ? |

No. |

The characteristic equation for 43 is . r= 0 is a root. so that and [tex]r= -2- \sqrt{3}[tex] are the other 2 roots. The general solution to the differential equation is . You forgot the constant solution. For 44 if you set y= x, then y'= 1 and y''= 0 so the equation becomes x(0)- 1+ 1= 0. If y= sin(x+ c) then y'= cos(x+ c) and y''= -sin(x+ c). The equation becomes . If y= sinh(x+ c) then y'= cosh(x+ c) and y''= sinh(x+ c). The equation becomes [tex]sinh^2(x+ c)- cosh^2(x+ c)+ 1= 0. |

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