# Why does the DSolve not solve the PDE giving the 'Arbitrary functions'?

Posted 1 month ago
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 Hello, I have two PDEs (strainDisp11 & strainDisp22) in 2 variables x1 and x2. strainDisp11 is a PDE with the partial differential term in x1 whereas, strainDisp22 is a PDE with the partial differential term in x2 I am trying to solve these two PDEs separately using DSolve (Last two command lines in the attached file), however, the solution is not generated along with the required arbitrary functions C1 which should be f1[x2] and C1 which should be f2[x1] in the respective solutions of the PDEs. Attached is Notebook for your reference. Appreciate your help. Answer
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Posted 1 month ago
 A Tip: Don't use Subscript , because causes problems. Answer
Posted 1 month ago
 Thanks! Very much appreciated. Answer
Posted 11 days ago
 Hello, I have two PDEs in 2 variables 'r' and 'theta'. I am trying to solve these two PDEs separately using DSolve (The last two command lines in the attached file). The solution is generated as expected for the 1st PDE (Integration with respect to variable 'r'), however, the solution is not generated for the 2nd PDE (Integration with respect to 'theta'). I cannot understand why Mathematica does not solve all the terms and has replaced 'theta' by K in the unsolved integral with limits? Attached is Notebook for your reference. Appreciate your help. Answer
Posted 11 days ago
 Maybe: solDispRR = DSolve[strainDispRR == 0, uR, {r, \[Theta]}] // Flatten; solDisp\[Theta]\[Theta] = DSolve[strainDisp\[Theta]\[Theta] == 0, u\[Theta], {r, \[Theta]}] // Flatten; uRFunctionTemp = uR[r, \[Theta]] /. solDispRR[] u\[Theta]FunctionTemp = (u\[Theta][r, \[Theta]] /. solDisp\[Theta]\[Theta][] /. solDispRR[]) // Activate // ExpandAll Looks like MMA can't integrate, a workaround: u\[Theta]FunctionTemp = (Integrate[#, {K, 1, \[Theta]}] & /@ (u\[Theta]FunctionTemp[[1, 1]])) + u\[Theta]FunctionTemp[] (*Integrate[-C[K], {K, 1, \[Theta]}] + (2*P*\[Nu]^2*Log[r]*(Sin - Sin[\[Theta]]))/(Pi*\[DoubleStruckCapitalE]) + (2*P*\[Nu]*(-Sin + Sin[\[Theta]]))/(Pi*\[DoubleStruckCapitalE]) + (2*P*\[Nu]^2*(-Sin + Sin[\[Theta]]))/(Pi*\[DoubleStruckCapitalE]) + (2*P*Log[r]*(-Sin + Sin[\[Theta]]))/(Pi*\[DoubleStruckCapitalE]) + C[r]*) In this line: Integrate[-C[K], {K, 1, \[Theta]}] what answer do you expect? Answer
Posted 11 days ago
 The expression is not complicated So as I want the DSolve (Integration with respect to Theta) to result in three terms as follows; But, I cannot understand why is MMA causing a definite integral with limits [1 to Theta], besides changing the variable 'Theta' to 'K' Answer
Posted 11 days ago
 Actually, to not confuse... the below is problem defined as PDE  The required solution for uTheta, upon Integrating with respect to Theta, we should get  Answer