11. Write general solution of the differential equation y" + a₁y' + aoy = 0 o Ax² + Bx + C o Axı + Bx^₂ + Сx¹³ Cx^3 o Ax
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paper?
I mean why are integral equations converted
to exponential functions?
I don't understand the implicative meaning. I want to know this
logic clearly
11. Write general solution of the differential equation y" + a₁y' + aoy = 0 o Ax² + Bx + C o Axı + Bx^₂ + Сx¹³ Cx^3 o Ax^¹ + Bx¹₂ • Aе¹¹ + Be¹₂x o Ae ¹x o explicit algebraic form does not exist
Step I: Given that the Differential Equation y" + a₁ y² + ₂y = 0 O da D²y + a₁ Dy + ay =o (:-D)² = dan d 5 (D² + 9₁D + 90) y = 0 बैभ D² + a₂D + a₂ = 0 Step II first we find Auxialary Equation of equation [D=m] & in equation 1. for this put we get, m² + a₁m + ao = 0 _9₁ ± √√√a₁²-490 m= 2 m₁ = a₁ + 92²-4a0 (Say) 2 -a₁-√a₁²-4% f m₂ = =d₂ (Say) 2 Now the general Solution of equation (D is miar m₂ s y = = Ae + Be put, m₁=d₁ f m₂ = d₂ from step, we get. y = A edi +Bex where A, B are arbitrary Constant. о 1 is correct 21 or, Gay, Step III!. Hence, option Ĉ